A084267 Partial sums of a binomial quotient.

1, 2, 4, 7, 11, 17, 24, 33, 44, 57, 72, 89, 109, 131, 156, 184, 215, 250, 288, 330, 376, 426, 480, 538, 601, 668, 740, 817, 899, 987, 1080, 1179, 1284, 1395, 1512, 1635, 1765, 1901, 2044, 2194, 2351, 2516, 2688, 2868, 3056, 3252, 3456, 3668, 3889, 4118, 4356

Offset: 0

Author

Paul Barry, Jun 01 2003

Keywords

• easy
• nonn

Comments

Partial sums of A011865 are a(n)=sum{k=0..n, floor(C(k+2,4)/C(k+2,2))}.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-3,3,-2,3,-3,2,-3,3,-1).

Programs

Mathematica

Accumulate[Table[Floor[Binomial[n,4]/Binomial[n,2]],{n,6,70}]]  (* Harvey P. Dale, Jul 19 2012 *)

Formula

a(n)=sum{k=0..n, floor(C(k+4, 4)/C(k+2, 2))}

G.f.: (x^4-x^3+x^2-x+1)/[(1-x)^4(1+x^2)(1+x+x^2)(1-x^2+x^4)].