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

Author

M. F. Hasler, May 03 2015

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A005062.

Coincides with A125373 only for the first terms.

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

Programs

Magma

[5*6^n-4*5^n: n in [0..20]]; // Vincenzo Librandi, May 04 2015

Mathematica

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

PARI

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

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