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

Author

Colin Barker, Feb 04 2015

Keywords

• nonn
• easy

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.

Examples

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

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).

Crossrefs

Cf. A000326, A069099, A254652, A254654.

Programs

PARI

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

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)).