A014769 Squares of odd pentagonal numbers.

1, 25, 1225, 2601, 13689, 21025, 61009, 82369, 180625, 227529, 423801, 511225, 855625, 1002001, 1555009, 1782225, 2614689, 2948089, 4141225, 4609609, 6255001, 6890625, 9090225, 9928801, 12794929, 13875625, 17530969, 18896409, 23474025, 25170289, 30813601

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).

Formula

a(n) = A014632(n)^2. - Sean A. Irvine, Nov 20 2018

From Colin Barker, Nov 20 2018: (Start)

G.f.: (1 + 24*x + 1196*x^2 + 1280*x^3 + 6294*x^4 + 1976*x^5 + 2828*x^6 + 176*x^7 + 49*x^8) / ((1 - x)^5*(1 + x)^4).

a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9) for n>8.

a(n) = 36*n^4 + 60*n^3 + 37*n^2 + 10*n + 1 for n even.

a(n) = 36*n^4 - 12*n^3 + n^2 for n odd.

(End)

Mathematica

Select[Table[PolygonalNumber[5, n]^2, {n, 0, 61}], OddQ] (* James C. McMahon, Dec 24 2023 *)

Prog

(PARI) Vec((1 + 24*x + 1196*x^2 + 1280*x^3 + 6294*x^4 + 1976*x^5 + 2828*x^6 + 176*x^7 + 49*x^8) / ((1 - x)^5*(1 + x)^4) + O(x^40)) \\ Colin Barker, Nov 20 2018

Crossrefs

Cf. A014632.

Odd terms of A100255.

Sequence in context: A012799 A120694 A012809 * A012851 A181719 A096330

Adjacent sequences: A014766 A014767 A014768 * A014770 A014771 A014772

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)

Status

approved