A011924 Floor[n(n-1)(n-2)(n-3)/14].

0, 0, 0, 0, 1, 8, 25, 60, 120, 216, 360, 565, 848, 1225, 1716, 2340, 3120, 4080, 5245, 6644, 8305, 10260, 12540, 15180, 18216, 21685, 25628, 30085, 35100, 40716, 46980, 53940, 61645, 70148, 79501, 89760

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Edward Jiang, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1, 0, 0, 1, -4, 6, -4, 1).

Programs

Maple

seq(floor(n*(n-1)*(n-2)*(n-3)/14), n = 0 .. 100); # Robert Israel, Aug 05 2014

Mathematica

Table[Floor[(n(n-1)(n-2)(n-3))/14],{n,0,40}] (* or *) LinearRecurrence[ {4,-6,4,-1,0,0,1,-4,6,-4,1},{0,0,0,0,1,8,25,60,120,216,360},41] (* Harvey P. Dale, Jul 07 2011 *)

PARI

a(n)=floor(n*(n-1)*(n-2)*(n-3)/14) \\ Edward Jiang , Aug 05 2014

PARI

a(n)=binomial(n,4)*12\7 \\ Charles R Greathouse IV, May 27 2015

Formula

a(n) = +4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +a(n-7) -4*a(n-8) +6*a(n-9) -4*a(n-10) +a(n-11). G.f.: x^4*(x^6+4*x^5-x^4+4*x^3-x^2+4*x+1) / ((1-x)^5*(x^6+x^5+x^4+x^3+x^2+x+1) ). - R. J. Mathar, Apr 15 2010