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

0,2

Comments

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

Links

Table of n, a(n) for n=0..50.

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

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)].

Mathematica

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

Crossrefs

Sequence in context: A178063 A095233 A062434 * A177116 A011911 A175822

Adjacent sequences: A084264 A084265 A084266 * A084268 A084269 A084270

Keyword

easy,nonn

Author

Paul Barry, Jun 01 2003

Status

approved