%I #14 Nov 17 2023 21:44:49

%S 1,14,154,1526,14266,128534,1129114,9738806,82851706,697402454,

%T 5821341274,48265581686,397988613946,3266956634774,26716987140634,

%U 217805235562166,1770927253556986,14366815611873494,116330307978911194,940412945418752246,7591696934462256826

%N a(n) = 7*8^n-6*7^n.

%C First differences of 8^n-7^n = A016177.

%C a(n-1) is the number of numbers with n digits having the largest digit equal to 7. Note that this is independent of the base b > 7.

%C Equivalently, number of n-letter words over a 8-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 (15,-56).

%F G.f.: (1-x)/((1-7*x)*(1-8*x)). - _Vincenzo Librandi_, May 04 2015

%F E.g.f.: exp(7*x)*(7*exp(x) - 6). - _Stefano Spezia_, Nov 15 2023

%t Table[7 8^n - 6 7^n, {n, 0, 30}] (* _Vincenzo Librandi_, May 04 2015 *)

%o (PARI) a(n)=7*8^n-6*7^n

%o (Magma) [7*8^n-6*7^n: n in [0..20]]; // _Vincenzo Librandi_, May 04 2015

%Y Cf. A016177.

%K nonn,easy

%O 0,2

%A _M. F. Hasler_, May 03 2015