A014797 Squares of odd square pyramidal numbers.

1, 25, 3025, 8281, 81225, 148225, 670761, 1030225, 3186225, 4447881, 10962721, 14402025, 30525625, 38452401, 73188025, 89397025, 156975841, 187279225, 308880625, 361722361, 567440041, 654592225, 985646025, 1122987121, 1634180625, 1842555625, 2604979521, 2911142025

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).

Formula

G.f.: -(x^12 +24*x^11 +2994*x^10 +5112*x^9 +54959*x^8 +35824*x^7 +129852*x^6 +35824*x^5 +54959*x^4 +5112*x^3 +2994*x^2 +24*x +1)/((x -1)^7*(x +1)^6). - Colin Barker, Nov 16 2012

a(n) = A015221(n)^2. - R. J. Mathar, Jul 30 2016

Sum_{n>=0} 1/a(n) = (171/4 - 18*sqrt(2))*Pi^2 - 54*Pi. - Amiram Eldar, Mar 07 2022

Mathematica

CoefficientList[Series[-(x^12+24x^11+2994x^10+5112x^9+54959x^8+35824x^7+ 129852x^6+ 35824x^5+54959x^4+5112x^3+2994x^2+24x+1)/((x-1)^7(x+1)^6), {x, 0, 30}], x] (* or *) LinearRecurrence[ {1, 6, -6, -15, 15, 20, -20, -15, 15, 6, -6, -1, 1}, {1, 25, 3025, 8281, 81225, 148225, 670761, 1030225, 3186225, 4447881, 10962721, 14402025, 30525625}, 30](* Harvey P. Dale, Feb 17 2013 *)

Crossrefs

Cf. A014798, A015221.

Sequence in context: A082488 A363865 A209850 * A077519 A078215 A075414

Adjacent sequences: A014794 A014795 A014796 * A014798 A014799 A014800

Keyword

nonn,easy

Author

Mohammad K. Azarian

Status

approved