A253878 Indices of triangular numbers (A000217) which are also centered heptagonal numbers (A069099).

1, 22, 358, 5713, 91057, 1451206, 23128246, 368600737, 5874483553, 93623136118, 1492095694342, 23779907973361, 378986431879441, 6040003002097702, 96261061601683798, 1534136982624843073, 24449930660395805377, 389664753583708042966, 6210186126678932882086

Offset: 1

Author

Colin Barker, Jan 17 2015

Keywords

• nonn
• easy

Comments

Also positive integers x in the solutions to x^2 - 7*y^2 + x + 7*y - 2 = 0, the corresponding values of y being A253879.

Examples

			22 is in the sequence because the 22nd triangular number is 253, which is also the 9th centered heptagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..832
• Index entries for linear recurrences with constant coefficients, signature (17,-17,1).

Crossrefs

Cf. A000217, A069099, A253879, A253880.

Programs

Mathematica

LinearRecurrence[{17,-17,1},{1,22,358},20] (* Harvey P. Dale, Sep 10 2022 *)

PARI

Vec(-x*(x^2+5*x+1)/((x-1)*(x^2-16*x+1)) + O(x^100))

Formula

a(n) = 17*a(n-1)-17*a(n-2)+a(n-3).

G.f.: -x*(x^2+5*x+1) / ((x-1)*(x^2-16*x+1)).

a(n) = (-2+(8-3*sqrt(7))^n*(3+sqrt(7))-(-3+sqrt(7))*(8+3*sqrt(7))^n)/4. - Colin Barker, Mar 04 2016