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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. 1
 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 Robert Israel, Table of n, a(n) for n = 1..3320 FORMULA a(n) = 2a(n-1) + (-1)^n a(ceiling(n/2)) for n >= 3. 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 + ... MAPLE f:= proc(n) option remember;     2*procname(n-1)+(-1)^n*procname(ceil(n/2)) end proc: f(1):= 0: f(2):= 2: map(f, [\$1..100]); # Robert Israel, Jul 15 2018 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: A167399 A247326 A300274 * A014113 A078008 A151575 Adjacent sequences:  A019307 A019308 A019309 * A019311 A019312 A019313 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 18 16:40 EST 2019. Contains 319271 sequences. (Running on oeis4.)