%I #15 Oct 18 2022 15:28:39
%S 0,0,0,0,2,13,40,93,186,336,560,880,1320,1906,2669,3640,4853,6346,
%T 8160,10336,12920,15960,19506,23613,28336,33733,39866,46800,54600,
%U 63336,73080,83906,95893,109120,123669,139626,157080,176120,196840,219336,243706,270053,298480
%N a(n) = floor(n*(n-1)*(n-2)*(n-3)/9).
%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 _R. J. Mathar_, Apr 15 2010: (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).
%F G.f.: x^4*(2 + 5*x + 3*x^3 + 4*x^4 + 3*x^5 + 5*x^7 + 2*x^8) / ( (1-x)^5*(1+x+x^2)*(x^6+x^3+1) ). (End)
%t Table[Floor[n(n-1)(n-2)(n-3)/9],{n,0,40}] (* or *) LinearRecurrence[ {4,-6,4,-1,0,0,0,0,1,-4,6,-4,1},{0,0,0,0,2,13,40,93,186,336,560,880,1320},40] (* _Harvey P. Dale_, Jan 01 2019 *)
%o (PARI) a(n) = floor(n*(n-1)*(n-2)*(n-3)/9); \\ _Jinyuan Wang_, Feb 28 2020
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_
%E More terms from _Jinyuan Wang_, Feb 28 2020