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

1,2

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.

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).

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)).

Example

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

Prog

(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))

Crossrefs

Cf. A000566, A005448, A254674, A254676.

Sequence in context: A159742 A098385 A048364 * A141549 A121964 A147208

Adjacent sequences: A254672 A254673 A254674 * A254676 A254677 A254678

Keyword

nonn,easy

Author

Colin Barker, Feb 05 2015

Status

approved