A253599 Centered square numbers (A001844) which are also centered heptagonal numbers (A069099).

1, 841, 43513, 54236113, 2807177521, 3498988573081, 181102250526121, 225733748749491361, 11683630587634972513, 14562987063325697070313, 753757743549580366157401, 939516547177660272044661361, 48627927055673997154643575441, 60611970510056587727363585953081

Offset: 1

Author

Colin Barker, Jan 05 2015

Keywords

• nonn
• easy

Examples

			841 is in the sequence because it is the 21st centered square number and the 16th centered heptagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..416
• Index entries for linear recurrences with constant coefficients, signature (1,64514,-64514,-1,1).

Crossrefs

Cf. A001844, A069099, A253459, A253460.

Programs

Mathematica

LinearRecurrence[{1,64514,-64514,-1,1},{1,841,43513,54236113,2807177521},20] (* Harvey P. Dale, Mar 26 2023 *)

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))

Formula

a(n) = a(n-1)+64514*a(n-2)-64514*a(n-3)-a(n-4)+a(n-5).

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)).