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Squares of odd hexagonal pyramidal numbers.
1

%I #27 Feb 07 2024 12:56:09

%S 1,49,9025,25921,275625,511225,2393209,3705625,11675889,16378209,

%T 40844881,53831569,115025625,145226601,278055625,340218025,600103009,

%U 716900625,1186595809,1391066209,2188461961,2526771289,3813680025

%N Squares of odd hexagonal pyramidal numbers.

%H Vincenzo Librandi, <a href="/A014801/b014801.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).

%F 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]

%F a(n) = A015225(n)^2. - _R. J. Mathar_, Jul 30 2016

%F a(n) == 1 (mod 8). - _Hugo Pfoertner_, Feb 07 2024

%t 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 *)

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_