Summary

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	File:     genrfncs.icn

	Subject:  Procedures to generate sequences

	Author:   Ralph E. Griswold

	Date:     June 10, 2001

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   This file is in the public domain.

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  These procedures generate sequences of results.

  arandseq(i, j)	arithmetic sequence starting at i with randomly
			chosen increment between 1 and j
  
  arithseq(i, j)	arithmetic sequence starting at i with increment j

  beatty1seq()		Beatty's first sequence i * &phi

  beatty2seq()		Beatty's second sequence i * &phi ^ 2

  catlnseq(i)		sequence of generalized Catalan numbers

  cfseq(i, j)		continued-fraction sequence for i / j

  chaosseq()		chaotic sequence

  chexmorphseq()	sequence of centered hexamorphic numbers

  connellseq(p)	generalized Connell sequence

  dietzseq(s)		Dietz sequence for polynomial

  dressseq(i)		dress sequence with increment i, default 1 (Schroeder)

  eisseq(i)		EIS A sequence for i

  factseq()		factorial sequence

  fareyseq(i, k)	Farey fraction sequence; k = 0, the default, produces
			numerator sequence; k = 1 produces denominator
			sequence

  fibseq(i, j, k, m)	generalized Fibonacci sequence (Lucas sequence)
			with initial values i and j and additive constant
			k.  If m is supplied, the results are produced
			mod m.

  figurseq(i)		series of ith figurate number

  fileseq(s, i)	generate from file s; if i is null, lines are generated.
			Otherwise characters, except line terminators.

  friendseq(k)		generate random friendly sequence from k values, 1 to k
			(in a friendly sequence, successive terms differ by 1).


  geomseq(i, j)	geometric sequence starting at i with multiplier j

  hailseq(i)		hailstone sequence starting at i

  irepl(i, j)		j instances of i

  lrrcseq(L1, L2)
			generalized linear recurrence with constant
			coefficients; L1 is a list of initial terms,
			L2 is a list of coefficients for n prevous values,
			where n = *L2

  meanderseq(s, n)	sequences of all characters that contain all n-tuples
			of characters from s
	
  mthueseq()		Morse-Thue sequence

  mthuegseq(i)		Morse-Thue sequence for base i

  multiseq(i, j, k)	sequence of (i * j + k) i's

  ngonalseq(i)		sequence of the ith polygonal number

  nibonacciseq(values[])
			generalized Fibonacci sequence that sums the
			previous n terms, where n = *values.

  partitseq(i, j, k)	sequence of integer partitions of i with minimum j
			and maximum k

  pellseq(i, j, k)	generalized Pell's sequence starting with i, j and
			using multiplier k

  perrinseq()		Perrin sequence

  polyseq(coeff[])	polynomial in x evaluated for x := seq()
	
  primeseq()		the sequence of prime numbers

  powerseq(i)		sequence n ^ i, n = 1, 2, 3, 4, ...

  powersofseq(i)	sequence i ^ n, n = 1, 2, 3, 4, ...n

  rabbitseq()		rabbit sequence

  ratsseq(i)		versumseq() with sort

  signaseq(r)		signature sequence of r

  spectseq(r)		spectral sequence integer(i * r), i - 1, 2, 3, ...

  srpseq(n, m)		palindromic part of the continued-fraction sequence
			for sqrt(n^2+m)

  versumseq(i, j)	generalized sequence of added reversed integers with
			seed i (default 196) and increment j (default 0)

  versumopseq(i, p)	procedure p (default 1) applied to versumseq(i)

  vishwanathseq()	random variation on Fibonacci sequence

  zebra(values[])	zebra colors, alternating 2 and 1, for number of
			times given by successive values
  
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  Requires:  co-expressions

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  Links:  convert, factors, fastfncs, io, lindgen, lists, numbers,
	partit, periodic, polynom, rational, strings, xcode

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This file is part of the (main) package.

arandseq(i, j)

: arithmetic sequence with random intervals

arithseq(i, j)

: arithmetic sequence

beatty1seq(r)

: Beatty sequence 1

beatty2seq(r)

: Beatty sequence 2

catlnseq(i)

: generalized Catalan sequence

cfseq(i, j)

: continued-fraction sequence

chaosseq()

: Hofstadter's chaotic sequence

chexmorphseq()

: sequence of centered hexamorphic numbers

connellseq(p, args)

: generalized Connell sequence

dietzseq(str)

dressseq(i)

: dress sequence

eisseq(i)

: EIS A sequence

eval(str)

factseq()

: factorial sequence

fareydseq(i)

: Farey fraction denominator sequence

fareyn1seq(i)

: Farey fraction numerator sequence, 1-based

fareynseq(i)

: Farey fraction numerator sequence

fareyseq(i, k)

: Farey fraction sequence

fibseq(i, j, k, m)

: generalized Fibonacci sequence

figurseq(i)

: sequence of figurate numbers

fileseq(s, i)

: sequence from file

form(str1, op, str2)

friendseq(k)

: random friendly sequence

geomseq(i, j)

: geometric sequence

hailseq(i)

: hailstone sequence

irepl(i, j)

: repeated sequence

linrecseq(terms, coeffs)

: synonym for lrrcseq

lrrcseq(terms, coeffs)

: linear recurrence sequence

meanderseq(alpha, n)

: generate meandering characters

mthuegseq(j)

: generalized Morse-Thue sequence

mthueseq()

: Morse-Thue sequence

multiseq(i, j, k)

: sequence of repeated integers

ngonalseq(i)

: sequence of polygonal numbers

nibonacciseq(values)

: n-valued Fibonacci generalization

oper(str)

partitseq(i, j, k)

: sequence of integer partitions

pellseq(i, j, k)

: generalized Pell sequence

perrinseq()

: perrin sequence

polyseq(coeff)

: sequence of polynomial evaluations

powerseq(i)

: powers sequence

powersofseq(i)

: powers

primeseq()

: sequence of prime numbers

rabbitseq()

: rabbit sequence

ratsseq(i, p)

: reverse add and then sort sequence

signaseq(r, n, m)

: signature sequence

spectseq(r)

: spectral sequence

srpseq(n, m)

: generate square-root palindrome

versumopseq(i, p, args)

: versum sequence with operator

versumseq(i, j)

: generalized reversed-sum sequence

vishwanathseq(i, j)

: random variation on Fibonacci sequence

zebra(args)

: black and white bands

entry(value, i, j)

farey(magnitude, n, d)