A048000 Number of nonempty subsets of {1,2,...,n} in which exactly 4/5 of the elements are <= n/3.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 10, 50, 55, 60, 180, 195, 210, 490, 525, 560, 1240, 1326, 1413, 3645, 3933, 4230, 12750, 13860, 15015, 45375, 49335, 53460, 150524, 163175, 176345, 470665, 509067, 549094, 1461278, 1580761

Offset

1,12

Links

Robert Israel, Table of n, a(n) for n = 1..5711

Formula

a(n) = Sum_{k=1..floor(n/5)} binomial(floor(n/3), 4*k)*binomial(ceiling(2*n/3), k). - Robert Israel, Feb 05 2017

Maple

f:= proc(n) local k;
  add(binomial(floor(n/3), 4*k/5)*binomial(n-floor(n/3), k/5), k=5..n, 5)
end proc:
map(f, [$1..60]); # Robert Israel, Feb 05 2017

Mathematica

Table[Sum[Binomial[Floor[n/3], 4 k]*Binomial[Ceiling[2 n/3], k], {k, Floor[n/5]}], {n, 50}] (* Wesley Ivan Hurt, Aug 04 2025 *)

Prog

(PARI) a(n)=sum(k=1, n\5, binomial(n\3, 4*k)*binomial(ceil(2*n/3), k)) \\ Charles R Greathouse IV, Feb 05 2017

Crossrefs

Sequence in context: A270039 A048020 A363760 * A048081 A109936 A114460

Adjacent sequences: A047997 A047998 A047999 * A048001 A048002 A048003

Keyword

nonn

Author

Clark Kimberling

Status

approved