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A019310 Number of words of length n (n >= 1) over a two-letter alphabet having a minimal period of size n-1. 0
0, 2, 2, 6, 10, 22, 38, 82, 154, 318, 614, 1250, 2462, 4962, 9842, 19766, 39378, 78910, 157502, 315322, 630030, 1260674, 2520098, 5041446, 10080430, 20163322, 40321682, 80648326, 161286810, 322583462, 645147158, 1290314082, 2580588786, 5161216950 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

H. Harborth, Endliche 0-1-Folgen mit gleichen Teilblöcken, J. für Reine Angewandte Math. 271 (1974), 139-154.

LINKS

Table of n, a(n) for n=1..34.

FORMULA

a(n) = 2a(n-1) + (-1)^n a(ceiling(n/2)) for n >= 2.

a(n) = a(n-1) + 2*a(n-2) if n >=4 even. a(n) = a(n-1) + 2*a(n-2) + 2*a((n-1)/2) if n>=7 == 3 (mod 4). Michael Somos, Jan 23 2014

EXAMPLE

G.f. = 2*x^2 + 2*x^3 + 6*x^4 + 10*x^5 + 22*x^6 + 38*x^7 + 82*x^8 + ...

PROG

(PARI) a(n) = if (n==1, 0, if (n==2, 2, 2*a(n-1) + (-1)^n*a(ceil(n/2)))) \\ Michel Marcus, May 25 2013

CROSSREFS

Sequence in context: A123757 A167399 A247326 * A014113 A078008 A151575

Adjacent sequences:  A019307 A019308 A019309 * A019311 A019312 A019313

KEYWORD

nonn

AUTHOR

Jeffrey Shallit

STATUS

approved

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Last modified December 10 09:47 EST 2016. Contains 278999 sequences.