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%I #21 Dec 10 2023 11:08:28
%S 1,12,114,978,7926,61962,472614,3541578,26190726,191733162,1392520614,
%T 10049975178,72163811526,516030592362,3677517616614,26134444136778,
%U 185292033880326,1311149786699562,9262681804120614,65346572412186378
%N a(n) = 6*7^n - 5*6^n.
%C First differences of 7^n - 6^n = A016169.
%C a(n-1) is the number of numbers with n digits having the largest digit equal to 6. Note that this is independent of the base b > 6.
%C Equivalently, number of n-letter words over a 7-letter alphabet {a,b,c,d,e,f,g}, 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 (13,-42).
%F From _Vincenzo Librandi_, May 04 2015: (Start)
%F G.f.: (1-x)/((1-6*x)*(1-7*x)).
%F a(n) = 13*a(n-1) - 42*a(n-2). (End)
%F E.g.f.: exp(6*x)*(6*exp(x) - 5). - _Stefano Spezia_, Nov 15 2023
%t Table[6 7^n - 5 6^n, {n, 0, 30}] (* _Vincenzo Librandi_, May 04 2015 *)
%t LinearRecurrence[{13,-42},{1,12},20] (* _Harvey P. Dale_, Dec 10 2023 *)
%o (PARI) a(n)=6*7^n-5*6^n
%o (Magma) [6*7^n-5*6^n: n in [0..30]]; // _Vincenzo Librandi_, May 04 2015
%Y Cf. A016169.
%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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