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

1, 46, 207, 14652, 66493, 4717738, 21410379, 1519096824, 6894075385, 489144459430, 2219870863431, 157502996839476, 714791523949237, 50715475837851682, 230160650840790723, 16330225716791401968, 74111014779210663409, 5258281965330993581854

Offset

1,2

Comments

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.

Links

Colin Barker, Table of n, a(n) for n = 1..797

Index entries for linear recurrences with constant coefficients, signature (1,322,-322,-1,1).

Formula

a(n) = a(n-1)+322*a(n-2)-322*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(45*x^3+161*x^2-45*x-1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)).

Example

46 is in the sequence because the 46th centered square number is 4141, which is also the 41st heptagonal number.

Mathematica

LinearRecurrence[{1, 322, -322, -1, 1}, {1, 46, 207, 14652, 66493}, 20] (* Harvey P. Dale, Sep 19 2022 *)

Prog

(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))

Crossrefs

Cf. A000566, A001844, A254228, A254230.

Sequence in context: A160334 A235550 A083358 * A234161 A234154 A251410

Adjacent sequences: A254226 A254227 A254228 * A254230 A254231 A254232

Keyword

nonn,easy

Author

Colin Barker, Jan 27 2015

Status

approved