A047164 Number of nonempty subsets of {1,2,...,n} in which exactly 3/4 of the elements are <= n/2.

0, 0, 0, 0, 0, 3, 4, 16, 20, 50, 60, 135, 161, 392, 476, 1232, 1512, 3864, 4740, 11850, 14520, 36300, 44572, 112519, 138567, 351351, 433433, 1098188, 1355900, 3433703, 4243148, 10758608, 13308416, 33794504, 41843256, 106344792, 131772372, 335061789, 415445184, 1056924666

Offset

1,6

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Formula

a(n) = Sum_{k>=1} binomial(floor(n/2), 3*k)*binomial(ceiling(n/2), k). - Andrew Howroyd, Apr 11 2021

Prog

(PARI) a(n) = {my(m=n\2); sum(k=1, m\3, binomial(m, 3*k)*binomial(n-m, k))} \\ Andrew Howroyd, Apr 11 2021

Crossrefs

Cf. A047161, A047163.

Sequence in context: A329890 A334319 A330299 * A304988 A108653 A316194

Adjacent sequences: A047161 A047162 A047163 * A047165 A047166 A047167

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(35) and beyond from Andrew Howroyd, Apr 11 2021

Status

approved