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%I #8 Mar 26 2023 09:11:43
%S 1,841,43513,54236113,2807177521,3498988573081,181102250526121,
%T 225733748749491361,11683630587634972513,14562987063325697070313,
%U 753757743549580366157401,939516547177660272044661361,48627927055673997154643575441,60611970510056587727363585953081
%N Centered square numbers (A001844) which are also centered heptagonal numbers (A069099).
%H Colin Barker, <a href="/A253599/b253599.txt">Table of n, a(n) for n = 1..416</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,64514,-64514,-1,1).
%F a(n) = a(n-1)+64514*a(n-2)-64514*a(n-3)-a(n-4)+a(n-5).
%F G.f.: -x*(x^4+840*x^3-21842*x^2+840*x+1) / ((x-1)*(x^2-254*x+1)*(x^2+254*x+1)).
%e 841 is in the sequence because it is the 21st centered square number and the 16th centered heptagonal number.
%t LinearRecurrence[{1,64514,-64514,-1,1},{1,841,43513,54236113,2807177521},20] (* _Harvey P. Dale_, Mar 26 2023 *)
%o (PARI) Vec(-x*(x^4+840*x^3-21842*x^2+840*x+1)/((x-1)*(x^2-254*x+1)*(x^2+254*x+1)) + O(x^100))
%Y Cf. A001844, A069099, A253459, A253460.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jan 05 2015