A254965 Indices of centered hexagonal numbers (A003215) that are also heptagonal numbers (A000566).

1, 2, 13, 34, 275, 736, 6027, 16148, 132309, 354510, 2904761, 7783062, 63772423, 170872844, 1400088535, 3751419496, 30738175337, 82360356058, 674839768869, 1808176413770, 14815736739771, 39697520746872, 325271368506083, 871537280017404, 7141154370394045

Offset

1,2

Comments

Also positive integers y in the solutions to 5*x^2 - 6*y^2 - 3*x + 6*y - 2 = 0, the corresponding values of x being A254964.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,22,-22,-1,1).

Formula

a(n) = a(n-1)+22*a(n-2)-22*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(x^3+11*x^2-x-1) / ((x-1)*(x^4-22*x^2+1)).

Example

13 is in the sequence because the 13th centered hexagonal number is 469, which is also the 14th heptagonal number.

Prog

(PARI) Vec(x*(x^3+11*x^2-x-1)/((x-1)*(x^4-22*x^2+1)) + O(x^100))

Crossrefs

Cf. A000566, A003215, A254964, A254966.

Sequence in context: A084910 A124024 A102229 * A038501 A009350 A063092

Adjacent sequences: A254962 A254963 A254964 * A254966 A254967 A254968

Keyword

nonn,easy

Author

Colin Barker, Feb 11 2015

Status

approved