cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A016147 Expansion of 1/((1-3*x)*(1-12*x)).

This page as a plain text file.
%I A016147 #29 Mar 08 2025 18:18:57
%S A016147 1,15,189,2295,27621,331695,3981069,47775015,573306741,6879700575,
%T A016147 82556465949,990677768535,11888133753861,142657606640655,
%U A016147 1711891284470829,20542695427998855,246512345179032981,2958148142277535935,35497777707717851709,425973332493776481975
%N A016147 Expansion of 1/((1-3*x)*(1-12*x)).
%H A016147 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (15,-36).
%F A016147 a(n) = 15*a(n-1) - 36*a(n-2). - _Vincenzo Librandi_, Mar 14 2011
%F A016147 a(n) = (4*12^n - 3^n)/3. - _Zak Seidov_, Mar 14 2011
%F A016147 E.g.f.: exp(3*x)*(4*exp(9*x) - 1)/3. - _Elmo R. Oliveira_, Mar 08 2025
%t A016147 Join[{a=1,b=15},Table[c=15*b-36*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2011 *)
%t A016147 LinearRecurrence[{15,-36},{1,15},20] (* _Harvey P. Dale_, Apr 30 2013 *)
%K A016147 nonn,easy
%O A016147 0,2
%A A016147 _N. J. A. Sloane_