A253477 Indices of centered heptagonal numbers (A069099) which are also centered triangular numbers (A005448).

1, 10, 46, 1045, 5005, 114886, 550450, 12636361, 60544441, 1389884770, 6659338006, 152874688285, 732466636165, 16814825826526, 80564670640090, 1849477966229521, 8861381303773681, 203425761459420730, 974671378744464766, 22374984282570050725

Offset

1,2

Comments

Also positive integers y in the solutions to 3*x^2 - 7*y^2 - 3*x + 7*y = 0, the corresponding values of x being A253476.

Links

Colin Barker, Table of n, a(n) for n = 1..980

Index entries for linear recurrences with constant coefficients, signature (1,110,-110,-1,1).

Formula

a(n) = a(n-1)+110*a(n-2)-110*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+9*x^3-74*x^2+9*x+1) / ((x-1)*(x^4-110*x^2+1)).

Example

10 is in the sequence because the 10th centered heptagonal number is 316, which is also the 15th centered triangular number.

Mathematica

LinearRecurrence[{1, 110, -110, -1, 1}, {1, 10, 46, 1045, 5005}, 30] (* Harvey P. Dale, Aug 13 2018 *)

Prog

(PARI) Vec(-x*(x^4+9*x^3-74*x^2+9*x+1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))

Crossrefs

Cf. A005448, A069099, A253476, A253689.

Sequence in context: A219597 A000832 A242462 * A143895 A281767 A323799

Adjacent sequences: A253474 A253475 A253476 * A253478 A253479 A253480

Keyword

nonn,easy

Author

Colin Barker, Jan 02 2015

Status

approved