A048070 - OEIS

%I #19 Sep 20 2025 22:32:15

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,9,10,60,66,231,252,672,728,1638,1764,3619,

%T 3885,8085,8712,20592,22440,60775,66924,189189,209209,571539,631770,

%U 1627120,1794688,4394908,4838064,11553234,12712974,30503474,33620424,82755474,91486250,231396375,256562124

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

%H David A. Corneth, <a href="/A048070/b048070.txt">Table of n, a(n) for n = 1..3000</a>

%e 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}.

%o (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

%K nonn,easy

%O 1,14

%A _Clark Kimberling_

%E Corrected by _Franklin T. Adams-Watters_, Oct 25 2006

%E More terms from _David A. Corneth_, Sep 17 2025