A014794 Squares of even octagonal numbers.

0, 64, 1600, 9216, 30976, 78400, 166464, 313600, 541696, 876096, 1345600, 1982464, 2822400, 3904576, 5271616, 6969600, 9048064, 11560000, 14561856, 18113536, 22278400, 27123264, 32718400, 39137536, 46457856, 54760000

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: 64*x*(1+20*x+29*x^2+4*x^3)/(1-x)^5. - Colin Barker, Jan 06 2012

a(n) = 16n^2*(3n-1)^2. - Vincenzo Librandi, Jan 07 2012

E.g.f.: 16*exp(x)*x*(4 + 46*x + 48*x^2 + 9*x^3). - Stefano Spezia, Apr 16 2022

Mathematica

Table[16*n^2*(3*n-1)^2, {n, 0, 30}] (* Vincenzo Librandi, Jan 07 2012 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 64, 1600, 9216, 30976}, 30] (* Harvey P. Dale, Nov 27 2015 *)

Prog

(Magma) [16*n^2*(3*n-1)^2: n in [1..50]]; // Vincenzo Librandi, Jan 07 2012
(PARI) a(n) = 16*n^2*(3*n-1)^2 \\ Vincenzo Librandi, Jan 07 2012

Crossrefs

Cf. A000567, A014641, A014642, A014793.

Sequence in context: A208313 A145218 A282526 * A224282 A224205 A162994

Adjacent sequences: A014791 A014792 A014793 * A014795 A014796 A014797

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Patrick De Geest, Aug 2000

a(8) corrected by Vincenzo Librandi, Jan 07 2012

Status

approved