A084267 - OEIS

%I #13 Jun 13 2015 00:51:04

%S 1,2,4,7,11,17,24,33,44,57,72,89,109,131,156,184,215,250,288,330,376,

%T 426,480,538,601,668,740,817,899,987,1080,1179,1284,1395,1512,1635,

%U 1765,1901,2044,2194,2351,2516,2688,2868,3056,3252,3456,3668,3889,4118,4356

%N Partial sums of a binomial quotient.

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

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,3,-2,3,-3,2,-3,3,-1).

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

%F 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)].

%t Accumulate[Table[Floor[Binomial[n,4]/Binomial[n,2]],{n,6,70}]]  (* _Harvey P. Dale_, Jul 19 2012 *)

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jun 01 2003