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%I #27 Sep 08 2022 08:44:39
%S 484,2500,63504,138384,894916,1493284,5569600,8156736,22562500,
%T 30580900,70090384,90250000,181764324,225660484,413552896,499611904,
%U 852056100,1007808516,1624090000,1888771600,2907582084,3335062500,4943777344,5605816384,8050755076
%N Squares of even hexagonal pyramidal numbers.
%H Vincenzo Librandi, <a href="/A014803/b014803.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.: -4*(289*x^10 +936*x^9 +20757*x^8 +19952*x^7 +110626*x^6 +44832*x^5 +99442*x^4 +15696*x^3 +14525*x^2 +504*x +121)/((x -1)^7*(x +1)^6). [_Colin Barker_, Nov 16 2012]
%F From _Wesley Ivan Hurt_, Aug 30 2015: (Start)
%F a(n) = a(n-1)+6*a(n-2)-6*a(n-3)-15*a(n-4)+15*a(n-5)+20*a(n-6)-20*a(n-7)-15*a(n-8)+15*a(n-9)+6*a(n-10)-6*a(n-11)-a(n-12)+a(n-13), n>12.
%F a(n) = ((4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9))^2/576.
%F a(n) = A015226(n)^2. (End)
%F E.g.f.: (512*x^6+11904*x^5+90408*x^4+269664*x^3+301086*x^2+98928*x+4797)*exp(x)/18 -(256*x^5-4320*x^4+21816*x^3-37452*x^2+18270*x-1305)*exp(-x)/6. - _Robert Israel_, Aug 31 2015
%p A014803:=n->((4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9))^2/576: seq(A014803(n), n=0..40); # _Wesley Ivan Hurt_, Aug 30 2015
%t CoefficientList[Series[- 4 (289 x^10 + 936 x^9 + 20757 x^8 + 19952 x^7 + 110626 x^6 + 44832 x^5 + 99442 x^4 + 15696 x^3 + 14525 x^2 + 504 x + 121)/((x - 1)^7 (x + 1)^6), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)
%t Table[((4*n + (-1)^n + 5)*(4*n + (-1)^n + 7)*(8*n + 2*(-1)^n + 9))^2/
%t 576, {n, 0, 40}] (* _Wesley Ivan Hurt_, Aug 30 2015 *)
%o (Magma) [((4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9))^2/576 : n in [0..40]]; // _Wesley Ivan Hurt_, Aug 30 2015
%Y Cf. A015226.
%K nonn,easy
%O 0,1
%A _Mohammad K. Azarian_
%E Corrected and extended by _James A. Sellers_
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