A048001 Number of nonempty subsets of {1,2,...,n} in which exactly 1/6 of the elements are <= n/3.

0, 0, 0, 0, 0, 0, 2, 12, 18, 63, 168, 224, 504, 1014, 1270, 2420, 4620, 5742, 12012, 27027, 35035, 84119, 199304, 260064, 601664, 1339464, 1720944, 3755844, 8093214, 10329750, 22591800, 49876200, 64071194, 144780009

Offset

1,7

Links

Robert Israel, Table of n, a(n) for n = 1..3633

Formula

a(n) = Sum_{k=1..ceiling(2*n/3)/5} binomial(floor(n/3),k)*binomial(ceiling(2*n/3),5*k). - Robert Israel, Nov 12 2018

Maple

f:= proc(n) local n3, k;
  n3:= floor(n/3);
  add(binomial(n3, k)*binomial(n-n3, 5*k), k=1..(n-n3)/5);
end proc:
map(f, [$1..50]); # Robert Israel, Nov 11 2018

Mathematica

Table[Sum[Binomial[Floor[n/3], k]*Binomial[n-Floor[n/3], 5*k], {k, 1, n-Floor[n/3]}], {n, 1, 40}] (* G. C. Greubel, Nov 11 2018 *)

Prog

(PARI) vector(40, n, sum(k=1, n-n\3, binomial(n\3, k)*binomial(n - n\3, 5*k))) \\ G. C. Greubel, Nov 11 2018
(Magma) [(&+[Binomial(Floor(n/3), k)*Binomial(n - Floor(n/3), 5*k): k in [1..(n - Floor(n/3))]]): n in [1..40]];  // G. C. Greubel, Nov 11 2018

Crossrefs

Sequence in context: A066238 A101074 A115109 * A109299 A216629 A337290

Adjacent sequences: A047998 A047999 A048000 * A048002 A048003 A048004

Keyword

nonn

Author

Clark Kimberling

Status

approved