A257286 a(n) = 5*6^n - 4*5^n.

1, 10, 80, 580, 3980, 26380, 170780, 1087180, 6835580, 42575980, 263268380, 1618672780, 9907349180, 60420657580, 367406757980, 2228854610380, 13495197974780, 81581539411180, 492540994279580, 2970504754739980, 17899322473752380

Offset

0,2

Comments

First differences of 6^n - 5^n = A005062.

a(n-1) is the number of numbers with n digits having the largest digit equal to 5. Or, equivalently, number of n-letter words over a 6-letter alphabet {a,b,c,d,e,f}, which must not start with the first letter of the alphabet, and in which the last letter of the alphabet must appear.

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (11,-30).

Formula

a(n) = 11 a(n-1) - 30 a(n-2).

G.f.: (1-x)/((1-5*x)*(1-6*x)). - Vincenzo Librandi, May 04 2015

E.g.f.: exp(5*x)*(5*exp(x) - 4). - Stefano Spezia, Nov 15 2023

Mathematica

Table[5 6^n - 4 5^n, {n, 0, 30}] (* Vincenzo Librandi, May 04 2015 *)

Prog

(PARI) a(n)=5*6^n-4*5^n
(Magma) [5*6^n-4*5^n: n in [0..20]]; // Vincenzo Librandi, May 04 2015

Crossrefs

Cf. A005062.

Coincides with A125373 only for the first terms.

See also A000225, A027649, A255463, A257285, A257286, A257287, A257288, A257289 and A088924.

Sequence in context: A036070 A374511 A377199 * A125373 A093145 A341917

Adjacent sequences: A257283 A257284 A257285 * A257287 A257288 A257289

Keyword

nonn,easy

Author

M. F. Hasler, May 03 2015

Status

approved