A254653 Indices of centered heptagonal numbers (A069099) which are also pentagonal numbers (A000326).

1, 3, 58, 276, 6325, 30303, 695638, 3333000, 76513801, 366599643, 8415822418, 40322627676, 925663952125, 4435122444663, 101814618911278, 487823146285200, 11198682416288401, 53656110968927283, 1231753251172812778, 5901684383435715876, 135481658946593117125

Offset

1,2

Comments

Also positive integers y in the solutions to 3*x^2 - 7*y^2 - x + 7*y - 2 = 0, the corresponding values of x being A254652.

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

Example

3 is in the sequence because the 3rd centered heptagonal number is 22, which is also the 4th pentagonal number.

Prog

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

Crossrefs

Cf. A000326, A069099, A254652, A254654.

Sequence in context: A335293 A041735 A156487 * A243510 A024218 A049661

Adjacent sequences: A254650 A254651 A254652 * A254654 A254655 A254656

Keyword

nonn,easy

Author

Colin Barker, Feb 04 2015

Status

approved