A048006 Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= (n-1)/3.

0, 0, 0, 3, 6, 10, 25, 45, 77, 175, 322, 570, 1245, 2325, 4213, 9031, 17061, 31421, 66547, 126763, 236203, 496063, 950818, 1787346, 3730293, 7184421, 13598053, 28243063, 54604081, 103918153, 215008363, 416990563, 797154723

Offset

1,4

Links

Robert Israel, Table of n, a(n) for n = 1..3325

Formula

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

Maple

f:= n ->  add(binomial(floor((n-1)/3), k/3)*binomial(n-floor((n-1)/3),
       2*k/3), k=3..n, 3):
map(f, [$1..100]); # Robert Israel, Feb 05 2017

Prog

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

Crossrefs

Sequence in context: A091616 A117224 A173957 * A364170 A211231 A302094

Adjacent sequences: A048003 A048004 A048005 * A048007 A048008 A048009

Keyword

nonn

Author

Clark Kimberling

Status

approved