A048070 Number of nonempty subsets of {1,2,...,n} in which exactly 5/6 of the elements are <= (n-4)/2.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 60, 66, 231, 252, 672, 728, 1638, 1764, 3619, 3885, 8085, 8712, 20592, 22440, 60775, 66924, 189189, 209209, 571539, 631770, 1627120, 1794688, 4394908, 4838064, 11553234, 12712974, 30503474, 33620424, 82755474, 91486250, 231396375, 256562124

Offset

1,14

Links

David A. Corneth, Table of n, a(n) for n = 1..3000

Example

a(14) = 9 as (n-4)/2 = 5 so a subset must have 5 numbers in [1, 5] and 1 number in [6, 14] giving the 9 subsets {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 5, 9}, {1, 2, 3, 4, 5, 10}, {1, 2, 3, 4, 5, 11}, {1, 2, 3, 4, 5, 12}, {1, 2, 3, 4, 5, 13}, {1, 2, 3, 4, 5, 14}.

Prog

(PARI) a(n) = {my(b = (n-4)\2, i, maxi = min(b\5, n-b), res); sum(i = 1, maxi, binomial(b, 5*i)*binomial(n-b, i))} \\ David A. Corneth, Sep 17 2025

Crossrefs

Sequence in context: A037954 A271062 A041174 * A341527 A167708 A372764

Adjacent sequences: A048067 A048068 A048069 * A048071 A048072 A048073

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Corrected by Franklin T. Adams-Watters, Oct 25 2006

More terms from David A. Corneth, Sep 17 2025

Status

approved