A253446 Indices of centered heptagonal numbers (A069099) which are also centered octagonal numbers (A016754).

1, 16, 465, 13920, 417121, 12499696, 374573745, 11224712640, 336366805441, 10079779450576, 302057016711825, 9051630721904160, 271246864640412961, 8128354308490484656, 243579382390074126705, 7299253117393733316480, 218734014139421925367681

Offset: 1

Author

Colin Barker, Jan 01 2015

Keywords

• nonn
• easy

Comments

Also positive integers x in the solutions to 7*x^2 - 8*y^2 - 7*x + 8*y = 0, the corresponding values of y being A253447.

Examples

			16 is in the sequence because the 16th centered heptagonal number is 841, which is also the 15th centered octagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..678
• Index entries for linear recurrences with constant coefficients, signature (31,-31,1).

Crossrefs

Cf. A016754, A069099, A253447, A253514.

Programs

Mathematica

LinearRecurrence[{31,-31,1},{1,16,465},20] (* Harvey P. Dale, Oct 04 2023 *)

PARI

Vec(x*(15*x-1)/((x-1)*(x^2-30*x+1)) + O(x^100))

Formula

a(n) = 31*a(n-1)-31*a(n-2)+a(n-3).

G.f.: x*(15*x-1) / ((x-1)*(x^2-30*x+1)).

a(n) = sqrt((-2-(15-4*sqrt(14))^n-(15+4*sqrt(14))^n)*(2-(15-4*sqrt(14))^(1+n)-(15+4*sqrt(14))^(1+n)))/(4*sqrt(7)). - Gerry Martens, Jun 04 2015