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

1,2

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.

Links

Colin Barker, Table of n, a(n) for n = 1..832

Index entries for linear recurrences with constant coefficients, signature (17,-17,1).

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000217, A069099, A253879, A253880.

Sequence in context: A016263 A001718 A199671 * A081127 A016196 A238318

Adjacent sequences: A253875 A253876 A253877 * A253879 A253880 A253881

Keyword

nonn,easy

Author

Colin Barker, Jan 17 2015

Status

approved