A196792 - OEIS

%I #32 Jan 17 2025 09:04:00

%S 1,2,15,184,2381,30942,402235,5229044,67977561,883708282,11488207655,

%T 149346699504,1941507093541,25239592216022,328114698808275,

%U 4265491084507564,55451384098598321,720867993281778162,9371283912663116095,121826690864620509224,1583746981240066619901

%N a(n) = A047848(10, n).

%H Vincenzo Librandi, <a href="/A196792/b196792.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-13).

%F a(n) = (13^n + 11)/12.

%F a(n) = 13*a(n-1) - 11, with a(0) = 1.

%F G.f.: (1-12*x)/((1-x)*(1-13*x)). - _Bruno Berselli_, Oct 11 2011

%F From _Elmo R. Oliveira_, Aug 30 2024: (Start)

%F E.g.f.: exp(x)*(exp(12*x) + 11)/12.

%F a(n) = 14*a(n-1) - 13*a(n-2) for n > 1. (End)

%t (13^Range[0,40] +11)/12 (* _G. C. Greubel_, Jan 17 2025 *)

%o (Magma) [(13^n+11)/12: n in [0..20]];

%o (Python)

%o def A196792(n): return (pow(13, n) + 11)//12

%o print([A196792(n) for n in range(41)]) # _G. C. Greubel_, Jan 17 2025

%Y Cf. A047848, A047849, A047850, A047851, A047852, A047853, A047854, A047855, A047856.

%Y Cf. A001022 (first differences).

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Oct 11 2011