A011850 a(n) = floor(binomial(n,4)/4).

0, 0, 0, 0, 0, 1, 3, 8, 17, 31, 52, 82, 123, 178, 250, 341, 455, 595, 765, 969, 1211, 1496, 1828, 2213, 2656, 3162, 3737, 4387, 5118, 5937, 6851, 7866, 8990, 10230, 11594, 13090, 14726, 16511, 18453, 20562

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-6,6,-10,10,-6,6,-10,10,-6,6,-10,10,-5,1).

Crossrefs

A column of triangle A011857.

Programs

Maple

seq(floor(binomial(n,4)/4), n=0.. 39); # Zerinvary Lajos, Jan 12 2009

Mathematica

Floor[Binomial[Range[0,50],4]/4] (* or *) LinearRecurrence[ {5,-10,10,-6,6,-10,10,-6,6,-10,10,-6,6,-10,10,-5,1},{0,0,0,0,0,1,3,8,17,31,52,82,123,178,250,341,455},50] (* Harvey P. Dale, Mar 25 2013 *)

Formula

a(n) = +5*a(n-1) -10*a(n-2) +10*a(n-3) -6*a(n-4) +6*a(n-5) -10*a(n-6) +10*a(n-7) -6*a(n-8) +6*a(n-9) -10*a(n-10) +10*a(n-11) -6*a(n-12) +6*a(n-13) -10*a(n-14) +10*a(n-15) -5*a(n-16) +a(n-17). [R. J. Mathar, Apr 15 2010]

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