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A257286
a(n) = 5*6^n - 4*5^n.
7
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.
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.
Sequence in context: A036070 A374511 A377199 * A125373 A093145 A341917
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, May 03 2015
STATUS
approved