A014801 Squares of odd hexagonal pyramidal numbers.

1, 49, 9025, 25921, 275625, 511225, 2393209, 3705625, 11675889, 16378209, 40844881, 53831569, 115025625, 145226601, 278055625, 340218025, 600103009, 716900625, 1186595809, 1391066209, 2188461961, 2526771289, 3813680025

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.: -(9*x^12 +160*x^11 +15402*x^10 +24624*x^9 +244415*x^8 +151296*x^7 +518380*x^6 +134944*x^5 +195863*x^4 +16608*x^3 +8970*x^2 +48*x +1)/((x -1)^7*(x +1)^6). [Colin Barker, Nov 16 2012]

a(n) = A015225(n)^2. - R. J. Mathar, Jul 30 2016

a(n) == 1 (mod 8). - Hugo Pfoertner, Feb 07 2024

Mathematica

CoefficientList[Series[- (9 x^12 + 160 x^11 + 15402 x^10 + 24624 x^9 + 244415 x^8 + 151296 x^7 + 518380 x^6 + 134944 x^5 + 195863 x^4 + 16608 x^3 + 8970 x^2 + 48 x + 1)/((x - 1)^7 (x + 1)^6), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 15 2013 *)

Crossrefs

Sequence in context: A206247 A180273 A351598 * A187406 A094199 A194023

Adjacent sequences: A014798 A014799 A014800 * A014802 A014803 A014804

Keyword

nonn,easy

Author

Mohammad K. Azarian

Status

approved