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.

A254710 Indices of centered square numbers (A001844) which are also pentagonal numbers (A000326).

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%I A254710 #5 Jun 13 2015 00:55:24
%S A254710 1,2,9,22,119,300,1651,4172,22989,58102,320189,809250,4459651,
%T A254710 11271392,62114919,156990232,865149209,2186591850,12049974001,
%U A254710 30455295662,167834486799,424187547412,2337632841179,5908170368100,32559025289701,82290197605982
%N A254710 Indices of centered square numbers (A001844) which are also pentagonal numbers (A000326).
%C A254710 Also positive integers y in the solutions to 3*x^2 - 4*y^2 - x + 4*y - 2 = 0, the corresponding values of x being A254709.
%H A254710 Colin Barker, <a href="/A254710/b254710.txt">Table of n, a(n) for n = 1..1000</a>
%H A254710 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,14,-14,-1,1).
%F A254710 a(n) = a(n-1)+14*a(n-2)-14*a(n-3)-a(n-4)+a(n-5).
%F A254710 G.f.: x*(x^3+7*x^2-x-1) / ((x-1)*(x^2-4*x+1)*(x^2+4*x+1)).
%e A254710 9 is in the sequence because the 9th centered square number is 145, which is also the 10th pentagonal number.
%o A254710 (PARI) Vec(x*(x^3+7*x^2-x-1)/((x-1)*(x^2-4*x+1)*(x^2+4*x+1)) + O(x^100))
%Y A254710 Cf. A000326, A001844, A254709, A254711.
%K A254710 nonn,easy
%O A254710 1,2
%A A254710 _Colin Barker_, Feb 06 2015