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.

A305650 a(n) = -1/3 * (u^n-1)*(v^n-1) with u = 1+sqrt(3), v = 1-sqrt(3).

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%I A305650 #19 Jun 02 2019 11:27:05
%S A305650 1,1,9,13,61,117,421,949,2997,7381,21781,56277,160213,424789,1186389,
%T A305650 3189589,8817493,23883093,65663317,178568533,489512277,1334064469,
%U A305650 3651347797,9962435925,27244344661,74380006741,203315811669,555257419093,1517414896981,4144807761237
%N A305650 a(n) = -1/3 * (u^n-1)*(v^n-1) with u = 1+sqrt(3), v = 1-sqrt(3).
%H A305650 Colin Barker, <a href="/A305650/b305650.txt">Table of n, a(n) for n = 1..1000</a>
%H A305650 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-2,-4).
%F A305650 a(n) = a(n-1) + 6*a(n-2) - 2*a(n-3) - 4*a(n-4) for n > 4.
%F A305650 G.f.: x*(1 + 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 2*x - 2*x^2)). - _Colin Barker_, Jun 07 2018
%t A305650 LinearRecurrence[{1,6,-2,-4},{1,1,9,13},30] (* _Harvey P. Dale_, Jun 02 2019 *)
%o A305650 (PARI) Vec(x*(1 + 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 2*x - 2*x^2)) + O(x^40)) \\ _Colin Barker_, Jun 07 2018
%Y A305650 Cf. A129744.
%K A305650 nonn,easy
%O A305650 1,3
%A A305650 _Seiichi Manyama_, Jun 07 2018