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

1,2

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.

Links

Colin Barker, Table of n, a(n) for n = 1..678

Index entries for linear recurrences with constant coefficients, signature (31,-31,1).

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A016754, A069099, A253447, A253514.

Sequence in context: A318937 A358569 A368772 * A159646 A113674 A281834

Adjacent sequences: A253443 A253444 A253445 * A253447 A253448 A253449

Keyword

nonn,easy

Author

Colin Barker, Jan 01 2015

Status

approved