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

1,2

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.

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A005448, A069099, A253477, A253689.

Sequence in context: A320917 A343871 A000475 * A308596 A145053 A168298

Adjacent sequences: A253473 A253474 A253475 * A253477 A253478 A253479

Keyword

nonn,easy

Author

Colin Barker, Jan 02 2015

Status

approved