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

Author

Colin Barker, Jan 27 2015

Keywords

• nonn
• easy

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.

Examples

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

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).

Crossrefs

Cf. A000566, A001844, A254228, A254230.

Programs

Mathematica

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

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))

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)).