A047196 Number of nonempty subsets of {1,2,...,n} in which exactly 1/4 of the elements are <= n/3.

0, 0, 0, 1, 4, 8, 20, 41, 63, 126, 252, 392, 844, 1780, 2800, 5995, 12545, 19595, 41951, 88634, 138866, 299411, 636524, 997640, 2154104, 4594244, 7201692, 15584085, 33355944, 52311408, 113406028, 243374923, 381766253, 828748052

Offset

1,5

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Formula

a(n) = Sum_{1<=j<=n/4} binomial(floor(n/3),j)*binomial(n-floor(n/3),3*j). - Robert Israel, Dec 15 2020

Maple

f:= proc(n) local t, k;
add(binomial(floor(n/3), k)*binomial(n-floor(n/3), 3*k), k=1..n/4)
end proc:
map(f, [$1..50]); # Robert Israel, Dec 15 2020

Crossrefs

Sequence in context: A008136 A357060 A254128 * A009889 A334706 A095804

Adjacent sequences: A047193 A047194 A047195 * A047197 A047198 A047199

Keyword

nonn

Author

Clark Kimberling

Status

approved