%I #16 Oct 18 2022 15:28:21
%S 0,0,0,0,1,6,20,46,93,168,280,440,660,953,1334,1820,2426,3173,4080,
%T 5168,6460,7980,9753,11806,14168,16866,19933,23400,27300,31668,36540,
%U 41953,47946,54560,61834,69813,78540,88060,98420,109668,121853,135026,149240
%N a(n) = floor(n(n-1)(n-2)(n-3)/18).
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1, 0, 0, 0, 0, 1, -4, 6, -4, 1).
%F From _Chai Wah Wu_, Aug 02 2020: (Start)
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-9) - 4*a(n-10) + 6*a(n-11) - 4*a(n-12) + a(n-13) for n > 12.
%F G.f.: x^4*(-x^8 - 2*x^7 - 2*x^6 + 2*x^5 - 6*x^4 + 2*x^3 - 2*x^2 - 2*x - 1)/((x - 1)^5*(x^2 + x + 1)*(x^6 + x^3 + 1)). (End)
%t Table[Floor[n(n - 1)(n - 2)(n - 3)/18], {n, 0, 50}] (* _Stefan Steinerberger_, Apr 25 2006 *)
%o (PARI) a(n)=n*(n-1)*(n-2)*(n-3)\18 \\ _Charles R Greathouse IV_, Oct 18 2022
%K nonn,easy
%O 0,6
%A _N. J. A. Sloane_
%E More terms from _Stefan Steinerberger_, Apr 25 2006
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