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

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000567, A014641, A014642, A014793.

Programs

Magma

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

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 *)
Select[PolygonalNumber[8,Range[0,50]],EvenQ]^2 (* Harvey P. Dale, Aug 03 2025 *)

PARI

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

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

Extensions

More terms from Patrick De Geest, Aug 2000

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