A254675 Indices of centered triangular numbers (A005448) which are also heptagonal numbers (A000566).

1, 13, 44, 776, 2697, 48069, 167140, 2979472, 10359953, 184679165, 642149916, 11447128728, 39802934809, 709537301941, 2467139808212, 43979865591584, 152922865174305, 2726042129376237, 9478750500998668, 168970632155735080, 587529608196743081

Offset: 1

Author

Colin Barker, Feb 05 2015

Keywords

• nonn
• easy

Comments

Also positive integers y in the solutions to 5*x^2 - 3*y^2 - 3*x + 3*y - 2 = 0, the corresponding values of x being A254674.

Examples

			13 is in the sequence because the 13th centered triangular number is 235, which is also the 10th heptagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,62,-62,-1,1).

Crossrefs

Cf. A000566, A005448, A254674, A254676.

Programs

PARI

Vec(x*(12*x^3+31*x^2-12*x-1)/((x-1)*(x^2-8*x+1)*(x^2+8*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+62*a(n-2)-62*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(12*x^3+31*x^2-12*x-1) / ((x-1)*(x^2-8*x+1)*(x^2+8*x+1)).