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A257286 a(n) = 5*6^n - 4*5^n. 7

%I #23 Nov 15 2023 19:05:15

%S 1,10,80,580,3980,26380,170780,1087180,6835580,42575980,263268380,

%T 1618672780,9907349180,60420657580,367406757980,2228854610380,

%U 13495197974780,81581539411180,492540994279580,2970504754739980,17899322473752380

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

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

%C 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.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-30).

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

%F G.f.: (1-x)/((1-5*x)*(1-6*x)). - _Vincenzo Librandi_, May 04 2015

%F E.g.f.: exp(5*x)*(5*exp(x) - 4). - _Stefano Spezia_, Nov 15 2023

%t Table[5 6^n - 4 5^n, {n, 0, 30}] (* _Vincenzo Librandi_, May 04 2015 *)

%o (PARI) a(n)=5*6^n-4*5^n

%o (Magma) [5*6^n-4*5^n: n in [0..20]]; // _Vincenzo Librandi_, May 04 2015

%Y Cf. A005062.

%Y Coincides with A125373 only for the first terms.

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

%K nonn,easy

%O 0,2

%A _M. F. Hasler_, May 03 2015

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Last modified March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)