A393986 - OEIS

%I #10 Mar 06 2026 08:06:43

%S 0,0,0,1,1,2,2,4,4,6,7,11,13,15,19,25,30,36,43,52,62,74,88,105,122,

%T 143,168,196,228,264,307,354,408,468,537,616,705,803,916,1043,1185,

%U 1343,1521,1719,1943,2192,2471,2783,3126,3509,3937,4411,4937,5520,6167,6883,7677

%N Number of partitions p of n into distinct parts such that max(p) >= 3*min(p).

%F G.f.: Sum_{i>=1} Sum_{j>=0} q^(4*i+j) * Product_{k=i+1..3*i+j-1} (1+q^k).

%e a(8) = 4 counts these partitions: 71, 62, 521, 431.

%Y Cf. A241063, A393970, A393971, A393985.

%Y Cf. A241036.

%K nonn

%O 1,6

%A _Seiichi Manyama_, Mar 05 2026