A254674 Indices of heptagonal numbers (A000566) which are also centered triangular numbers (A005448).

1, 10, 34, 601, 2089, 37234, 129466, 2307889, 8024785, 143051866, 497407186, 8866907785, 30831220729, 549605230786, 1911038277994, 34066657400929, 118453542014881, 2111583153626794, 7342208566644610, 130884088867460281, 455098477589950921

Offset

1,2

Comments

Also positive integers x in the solutions to 5*x^2 - 3*y^2 - 3*x + 3*y - 2 = 0, the corresponding values of y being A254675.

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*(x^4+9*x^3-38*x^2+9*x+1) / ((x-1)*(x^2-8*x+1)*(x^2+8*x+1)).

Example

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

Prog

(PARI) Vec(-x*(x^4+9*x^3-38*x^2+9*x+1)/((x-1)*(x^2-8*x+1)*(x^2+8*x+1)) + O(x^100))

Crossrefs

Cf. A000566, A005448, A254675, A254676.

Sequence in context: A219591 A272365 A230895 * A260336 A010818 A243939

Adjacent sequences: A254671 A254672 A254673 * A254675 A254676 A254677

Keyword

nonn,easy

Author

Colin Barker, Feb 05 2015

Status

approved