A253476 Indices of centered triangular numbers (A005448) which are also centered heptagonal numbers (A069099).

1, 15, 70, 1596, 7645, 175491, 840826, 19302360, 92483161, 2123084055, 10172306830, 233519943636, 1118861268085, 25685070715851, 123064567182466, 2825124258799920, 13535983528803121, 310737983397275295, 1488835123601160790, 34178353049441482476

Offset: 1

Author

Colin Barker, Jan 02 2015

Keywords

• nonn
• easy

Comments

Also positive integers x in the solutions to 3*x^2 - 7*y^2 - 3*x + 7*y = 0, the corresponding values of y being A253477.

Examples

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

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).

Crossrefs

Cf. A005448, A069099, A253477, A253689.

Programs

Mathematica

LinearRecurrence[{1,110,-110,-1,1},{1,15,70,1596,7645},30] (* Harvey P. Dale, Jun 14 2016 *)

PARI

Vec(x*(14*x^3+55*x^2-14*x-1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))

Formula

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

G.f.: x*(14*x^3+55*x^2-14*x-1) / ((x-1)*(x^4-110*x^2+1)).