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.

A254964 Indices of heptagonal numbers (A000566) that are also centered hexagonal numbers (A003215).

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%I A254964 #9 Apr 13 2018 14:10:15
%S A254964 1,2,14,37,301,806,6602,17689,144937,388346,3182006,8525917,69859189,
%T A254964 187181822,1533720146,4109474161,33671984017,90221249714,739249928222,
%U A254964 1980758019541,16229826436861,43486455180182,356316931682714,954721255944457,7822742670582841
%N A254964 Indices of heptagonal numbers (A000566) that are also centered hexagonal numbers (A003215).
%C A254964 Also positive integers x in the solutions to 5*x^2 - 6*y^2 - 3*x + 6*y - 2 = 0, the corresponding values of y being A254965.
%H A254964 Colin Barker, <a href="/A254964/b254964.txt">Table of n, a(n) for n = 1..1000</a>
%H A254964 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,22,-22,-1,1).
%F A254964 a(n) = a(n-1)+22*a(n-2)-22*a(n-3)-a(n-4)+a(n-5).
%F A254964 G.f.: -x*(x^2-3*x+1)*(x^2+4*x+1) / ((x-1)*(x^4-22*x^2+1)).
%e A254964 14 is in the sequence because the 14th heptagonal number is 469, which is also the 13th centered hexagonal number.
%t A254964 LinearRecurrence[{1,22,-22,-1,1},{1,2,14,37,301},30] (* _Harvey P. Dale_, Apr 13 2018 *)
%o A254964 (PARI) Vec(-x*(x^2-3*x+1)*(x^2+4*x+1)/((x-1)*(x^4-22*x^2+1)) + O(x^100))
%Y A254964 Cf. A000566, A003215, A254965, A254966.
%K A254964 nonn,easy
%O A254964 1,2
%A A254964 _Colin Barker_, Feb 11 2015