A190331 a(n) = 8*a(n-1) + 2*a(n-2), with a(0)=0, a(1)=1.

0, 1, 8, 66, 544, 4484, 36960, 304648, 2511104, 20698128, 170607232, 1406254112, 11591247360, 95542487104, 787522391552, 6491264106624, 53505157636096, 441023789302016, 3635200629688320, 29963652616110592, 246979622188261376, 2035764282738312192

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn
• easy

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).

Programs

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

Mathematica

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

PARI

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

Formula

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