A047161 Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= n/2.

0, 0, 1, 2, 6, 9, 21, 30, 70, 100, 235, 335, 791, 1127, 2681, 3822, 9150, 13050, 31401, 44802, 108262, 154517, 374715, 534963, 1301235, 1858155, 4531423, 6472167, 15818791, 22597759, 55339849, 79067374, 193962894, 277164294, 680963509, 973184312, 2394289028, 3422117189

Offset

1,4

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

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

Prog

(PARI) a(n) = {my(m=n\2); sum(k=1, (n+1)\4, binomial(m, k)*binomial(n-m, 2*k))} \\ Andrew Howroyd, Apr 11 2021

Crossrefs

Cf. A014495, A047162.

Sequence in context: A095967 A316429 A337639 * A318193 A048083 A127931

Adjacent sequences: A047158 A047159 A047160 * A047162 A047163 A047164

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved