A011919 a(n) = floor(n*(n-1)*(n-2)*(n-3)/9).

0, 0, 0, 0, 2, 13, 40, 93, 186, 336, 560, 880, 1320, 1906, 2669, 3640, 4853, 6346, 8160, 10336, 12920, 15960, 19506, 23613, 28336, 33733, 39866, 46800, 54600, 63336, 73080, 83906, 95893, 109120, 123669, 139626, 157080, 176120, 196840, 219336, 243706, 270053, 298480

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,0,0,0,0,1,-4,6,-4,1).

Programs

Mathematica

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 *)

PARI

a(n) = floor(n*(n-1)*(n-2)*(n-3)/9); \\ Jinyuan Wang, Feb 28 2020

Formula

From R. J. Mathar, Apr 15 2010: (Start)

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).

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)

Extensions

More terms from Jinyuan Wang, Feb 28 2020