A254710 Indices of centered square numbers (A001844) which are also pentagonal numbers (A000326).

1, 2, 9, 22, 119, 300, 1651, 4172, 22989, 58102, 320189, 809250, 4459651, 11271392, 62114919, 156990232, 865149209, 2186591850, 12049974001, 30455295662, 167834486799, 424187547412, 2337632841179, 5908170368100, 32559025289701, 82290197605982

Offset: 1

Author

Colin Barker, Feb 06 2015

Keywords

• nonn
• easy

Comments

Also positive integers y in the solutions to 3*x^2 - 4*y^2 - x + 4*y - 2 = 0, the corresponding values of x being A254709.

Examples

			9 is in the sequence because the 9th centered square number is 145, which is also the 10th pentagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,14,-14,-1,1).

Crossrefs

Cf. A000326, A001844, A254709, A254711.

Programs

PARI

Vec(x*(x^3+7*x^2-x-1)/((x-1)*(x^2-4*x+1)*(x^2+4*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+14*a(n-2)-14*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(x^3+7*x^2-x-1) / ((x-1)*(x^2-4*x+1)*(x^2+4*x+1)).