A014798 Squares of even square pyramidal numbers.

196, 900, 19600, 41616, 256036, 422500, 1537600, 2238016, 6100900, 8236900, 18696976, 24010000, 48024900, 59505796, 108493056, 130873600, 222308100, 262634436, 421891600, 490179600, 752624356, 862596900, 1275918400, 1445824576, 2072616676, 2326132900, 3246720400

Offset

0,1

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.: -4*(49*x^10 +176*x^9 +4381*x^8 +4448*x^7 +26290*x^6 +11232*x^5 +26290*x^4 +4448*x^3 +4381*x^2 +176*x +49)/((x -1)^7*(x +1)^6). - Colin Barker, Nov 16 2012

a(n) = A015222(n+1)^2. - R. J. Mathar, Jul 30 2016

Sum_{n>=0} 1/a(n) = (165/4 + 18*sqrt(2))*Pi^2 + 54*Pi - 828. - Amiram Eldar, Mar 07 2022

Mathematica

CoefficientList[Series[- 4 (49 x^10 + 176 x^9 + 4381 x^8 + 4448 x^7 + 26290 x^6 + 11232 x^5 + 26290 x^4 + 4448 x^3 + 4381 x^2 + 176 x + 49)/((x - 1)^7 (x + 1)^6), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 15 2013 *)
Select[Table[n*(n + 1)*(2*n + 1)/6, {n, 1, 70}], EvenQ]^2 (* Amiram Eldar, Mar 07 2022 *)

Crossrefs

Cf. A014797, A015222.

Sequence in context: A063048 A306232 A006960 * A366278 A251308 A251301

Adjacent sequences: A014795 A014796 A014797 * A014799 A014800 A014801

Keyword

nonn,easy

Author

Mohammad K. Azarian

Status

approved