A155455 a(n) = 5*a(n-1)+16*a(n-2), n>1 ; a(0)=0, a(1)=1.

0, 1, 5, 41, 285, 2081, 14965, 108121, 780045, 5630161, 40631525, 293240201, 2116305405, 15273370241, 110227737685, 795512612281, 5741206864365, 41434236118321, 299030490421445, 2158100230000361, 15574988996744925, 112404548663730401, 811222567266570805

Offset: 0

Author

Philippe Deléham, Jan 22 2009

Keywords

• nonn
• easy

Comments

a(n+1) for n >= 0 is the number of compositions (ordered partitions) of n into parts 1 of 5 sorts and parts 2 of 16 sorts. - Joerg Arndt, Jan 29 2024

Links

• Index entries for linear recurrences with constant coefficients, signature (5,16).

Crossrefs

Cf. A015568 (binomial transform).

Programs

Mathematica

LinearRecurrence[{5, 16}, {0, 1}, 25] (* Paolo Xausa, Jan 29 2024 *)

Formula

G.f.: x/(1-5*x-16*x^2).

Extensions

Regularized: a(0) set to 0. - R. J. Mathar, Apr 01 2011

a(21)-a(22) from Paolo Xausa, Jan 29 2024