A394022 - OEIS

%I #11 Mar 07 2026 10:03:46

%S 1,2,3,3,4,5,5,6,7,7,7,10,10,12,14,14,16,19,20,22,25,25,29,33,35,38,

%T 42,44,48,56,58,63,70,74,80,88,93,102,111,118,126,138,145,157,171,180,

%U 194,211,224,238,256,271,291,314,333,356,379,402,429,461,486,517,552,584,622

%N Number of partitions p of n with multiplicity of each part at most 3, satisfying max(p) <= 2 * min(p).

%F G.f.: Sum_{j>=1} q^j*(1-q^(3*j))/(1-q^j) * Product_{k=j+1..2*j} (1-q^(4*k))/(1-q^k).

%e a(8) = 6 counts these partitions: 8, 53, 44, 422, 332, 22211.

%Y Cf. A237824, A241061, A394021.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Mar 07 2026