A186445 - OEIS

%I #9 Jul 14 2022 22:55:07

%S 1,1,1,1,1,2,3,4,5,6,8,10,13,16,20,25,31,38,47,57,70,85,103,124,150,

%T 180,216,258,308,366,436,516,611,721,850,1000,1176,1378,1614,1886,

%U 2203,2567,2990,3474,4034,4677,5417,6264,7239,8351,9628

%N The number of partitions of n in which the first part is at least four times larger than the second part.

%F a(n) = p(n)-p(n-2)-p(n-3)-p(n-4)+p(n-5)+p(n-6)+p(n-7)-p(n-9), where p(n) = A000041(n).

%e a(8) = #{8, 7+1, 6+1+1, 5+1+1+1, 4+1+1+1+1} = 5.

%e a(10) = #{10, 9+1, 8+2, 8+1+1, 7+1+1+1, 6+1+1+1+1, 5+1+1+1+1+1, 4+1+1+1+1+1+1} = 8.

%Y Cf. A000041.

%Y Partial sums of A185325.

%K nonn

%O 0,6

%A _Mircea Merca_, Feb 21 2011