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
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).
Programs
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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 *) LinearRecurrence[{1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1},{1,49,9025,25921,275625,511225,2393209,3705625,11675889,16378209,40844881,53831569,115025625},30] (* Harvey P. Dale, May 25 2025 *)
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