A196791 - OEIS

%I #34 Jan 17 2025 09:03:56

%S 1,2,14,158,1886,22622,271454,3257438,39089246,469070942,5628851294,

%T 67546215518,810554586206,9726655034462,116719860413534,

%U 1400638324962398,16807659899548766,201691918794585182,2420303025535022174,29043636306420266078,348523635677043192926

%N a(n) = A047848(9, n).

%H Vincenzo Librandi, <a href="/A196791/b196791.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 (13,-12).

%F a(n) = (12^n + 10)/11.

%F a(n) = 12*a(n-1) - 10, with a(0) = 1.

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

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

%F E.g.f.: exp(x)*(exp(11*x) + 10)/11.

%F a(n) = 13*a(n-1) - 12*a(n-2) for n > 1. (End)

%t LinearRecurrence[{13,-12},{1,2},30] (* _Harvey P. Dale_, Sep 07 2015 *)

%t (12^Range[0,40] +10)/11 (* _G. C. Greubel_, Jan 17 2025 *)

%o (Magma) [(12^n+10)/11: n in [0..20]];

%o (Python)

%o def A196791(n): return (pow(12, n) + 10)//11

%o print([A196791(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. A001021 (first differences).

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Oct 11 2011