A103455 a(n) = 0^n + 5^n - 1.

1, 4, 24, 124, 624, 3124, 15624, 78124, 390624, 1953124, 9765624, 48828124, 244140624, 1220703124, 6103515624, 30517578124, 152587890624, 762939453124, 3814697265624, 19073486328124, 95367431640624, 476837158203124

Offset: 0

Author

Paul Barry, Feb 06 2005

Keywords

• easy
• nonn

Comments

A transform of 5^n under the matrix A103452.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (6,-5).

Crossrefs

Cf. A024049, A103452.

Programs

Magma

[0^n+5^n-1: n in [0..30]]; // Vincenzo Librandi, Jun 06 2011

Mathematica

Join[{1},5^Range[20]-1] (* Harvey P. Dale, Nov 15 2011 *)

Sage

[1]+[5^n -1 for n in [1..40]] # G. C. Greubel, Jun 21 2021

Formula

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

a(n) = Sum_{k=0..n} A103452(n, k)*5^k.

a(n) = Sum_{k=0..n} (2*0^(n-k) - 1)*0^(k*(n-k))*5^k.

a(n) = A024049(n), n > 0. - R. J. Mathar, Aug 30 2008

E.g.f.: 1 - exp(x) + exp(5*x). - G. C. Greubel, Jun 21 2021