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

1,2

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.

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).

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)).

Example

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

Prog

(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))

Crossrefs

Cf. A000326, A001844, A254709, A254711.

Sequence in context: A025176 A032315 A032224 * A193758 A368626 A032149

Adjacent sequences: A254707 A254708 A254709 * A254711 A254712 A254713

Keyword

nonn,easy

Author

Colin Barker, Feb 06 2015

Status

approved