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%I #25 Nov 16 2023 19:07:53
%S 1,16,200,2248,23816,243016,2416520,23583688,226933256,2159839816,
%T 20378082440,190918934728,1778399954696,16486635929416,
%U 152228014061960,1400838452135368,12853836673840136,117654854901535816,1074656292809619080,9798007424852945608
%N a(n) = 8*9^n - 7*8^n.
%C First differences of 9^n - 8^n = A016185.
%C a(n-1) is the number of numbers with n digits having the largest digit equal to 8. Note that this is independent of the base b > 8.
%C Equivalently, number of n-letter words over a 9-letter alphabet, which must not start with the last letter of the alphabet, and in which the first letter of the alphabet must appear.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-72).
%F G.f.: (1-x)/((1-8*x)*(1-9*x)). - _Vincenzo Librandi_, May 04 2015
%F E.g.f.: exp(8*x)*(8*exp(x) - 7). - _Stefano Spezia_, Nov 15 2023
%t Table[8 9^n - 7 8^n, {n, 0, 20}] (* _Vincenzo Librandi_, May 04 2015 *)
%t LinearRecurrence[{17,-72},{1,16},30] (* _Harvey P. Dale_, May 26 2019 *)
%o (PARI) a(n)=8*9^n-7*8^n
%o (Magma) [8*9^n-7*8^n: n in [0..20]]; // _Vincenzo Librandi_, May 04 2015
%o (Sage) [8*9^n-7*8^n for n in (0..20)] # _Bruno Berselli_, May 04 2015
%Y Cf. A016185.
%Y See also A000225, A027649, A255463, A257285, A257286, A257287, A257288, and A088924.
%K nonn,easy
%O 0,2
%A _M. F. Hasler_, May 03 2015
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