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A190331 a(n) = 8*a(n-1) + 2*a(n-2), with a(0)=0, a(1)=1. 2
0, 1, 8, 66, 544, 4484, 36960, 304648, 2511104, 20698128, 170607232, 1406254112, 11591247360, 95542487104, 787522391552, 6491264106624, 53505157636096, 441023789302016, 3635200629688320, 29963652616110592, 246979622188261376, 2035764282738312192 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n>0, a(n) equals the number of words of length n-1 over {0,1,...,9} in which 0 and 1 avoid runs of odd lengths. - Milan Janjic, Jan 08 2017

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,2)

FORMULA

a(n) = (1/12)*sqrt(2)*((4+3*sqrt(2))^n - (4-3*sqrt(2))^n). - Paolo P. Lava, Nov 18 2011

G.f.: x/(1 - 8*x - 2*x^2). - R. J. Mathar, Nov 20 2011

MATHEMATICA

LinearRecurrence[{8, 2}, {0, 1}, 50]

PROG

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-8*x-2*x^2))) \\ G. C. Greubel, Jan 24 2018

(MAGMA) I:=[0, 1]; [n le 2 select I[n] else 8*Self(n-1) + 2*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 24 2018

CROSSREFS

Sequence in context: A121778 A037501 A037678 * A162758 A004331 A147959

Adjacent sequences:  A190328 A190329 A190330 * A190332 A190333 A190334

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, May 24 2011

STATUS

approved

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Last modified October 20 22:22 EDT 2021. Contains 348119 sequences. (Running on oeis4.)