A155616 a(n) = 5^n + 4^n - 1.

1, 8, 40, 188, 880, 4148, 19720, 94508, 456160, 2215268, 10814200, 53022428, 260917840, 1287811988, 6371951080, 31591319948, 156882857920, 780119322308, 3883416742360, 19348364235068, 96466943268400, 481235204714228, 2401777977060040, 11991297699255788, 59886119752101280

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-29,20).

Formula

G.f.: 1/(1-5*x)+1/(1-4*x)-1/(1-x).

E.g.f.: e^(5*x)+e^(4*x)-e^x.

a(n) = 9*a(n-1)-20*a(n-2)-12 with a(0)=1, a(1)=8. - Vincenzo Librandi, Jul 21 2010

Mathematica

A155616[n_] := 5^n + 4^n - 1; Array[A155616, 25, 0] (* Paolo Xausa, Mar 04 2026 *)

Prog

(PARI) a(n)=5^n+4^n-1 \\ Charles R Greathouse IV, Oct 16 2015

Crossrefs

Cf. A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615.

Sequence in context: A270458 A241304 A272274 * A270947 A271595 A270283

Adjacent sequences: A155613 A155614 A155615 * A155617 A155618 A155619

Keyword

nonn,easy

Author

Mohammad K. Azarian, Jan 27 2009

Extensions

More terms from Paolo Xausa, Mar 04 2026

Status

approved