A274072 a(n) = 5^n-(-1)^n.

0, 6, 24, 126, 624, 3126, 15624, 78126, 390624, 1953126, 9765624, 48828126, 244140624, 1220703126, 6103515624, 30517578126, 152587890624, 762939453126, 3814697265624, 19073486328126, 95367431640624, 476837158203126, 2384185791015624, 11920928955078126

Offset: 0

Author

Colin Barker, Jun 09 2016

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,5).

Crossrefs

Cf. A015531.

Sequences of the type k^n-(-1)^n: A062157 (k=0), A010673 (k=1), A062510 (k=2), A105723 (k=3), A247281 (k=4), this sequence (k=5), A274073 (k=6).

Programs

Mathematica

LinearRecurrence[{4, 5}, {0, 6}, 30] (* Paolo Xausa, Oct 21 2024 *)

PARI

concat(0, Vec(6*x/((1+x)*(1-5*x)) + O(x^30)))

Formula

O.g.f.: 6*x/((1+x)*(1-5*x)).

E.g.f.: exp(5*x) - exp(-x).

a(n) = 4*a(n-1) + 5*a(n-2) for n>1.

a(n) = 6*A015531(n).