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

1,2

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).

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)).

Example

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

Mathematica

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

Prog

(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))

Crossrefs

Cf. A001844, A069099, A253459, A253460.

Sequence in context: A108324 A133496 A361675 * A121499 A253514 A342841

Adjacent sequences: A253596 A253597 A253598 * A253600 A253601 A253602

Keyword

nonn,easy

Author

Colin Barker, Jan 05 2015

Status

approved