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.

A254229 Indices of centered square numbers (A001844) which are also heptagonal numbers (A000566).

This page as a plain text file.
%I A254229 #8 Sep 19 2022 13:41:15
%S A254229 1,46,207,14652,66493,4717738,21410379,1519096824,6894075385,
%T A254229 489144459430,2219870863431,157502996839476,714791523949237,
%U A254229 50715475837851682,230160650840790723,16330225716791401968,74111014779210663409,5258281965330993581854
%N A254229 Indices of centered square numbers (A001844) which are also heptagonal numbers (A000566).
%C A254229 Also positive integers y in the solutions to 5*x^2 - 4*y^2 - 3*x + 4*y - 2 = 0, the corresponding values of x being A254228.
%H A254229 Colin Barker, <a href="/A254229/b254229.txt">Table of n, a(n) for n = 1..797</a>
%H A254229 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,322,-322,-1,1).
%F A254229 a(n) = a(n-1)+322*a(n-2)-322*a(n-3)-a(n-4)+a(n-5).
%F A254229 G.f.: x*(45*x^3+161*x^2-45*x-1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)).
%e A254229 46 is in the sequence because the 46th centered square number is 4141, which is also the 41st heptagonal number.
%t A254229 LinearRecurrence[{1,322,-322,-1,1},{1,46,207,14652,66493},20] (* _Harvey P. Dale_, Sep 19 2022 *)
%o A254229 (PARI) Vec(x*(45*x^3+161*x^2-45*x-1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))
%Y A254229 Cf. A000566, A001844, A254228, A254230.
%K A254229 nonn,easy
%O A254229 1,2
%A A254229 _Colin Barker_, Jan 27 2015