A394283 - OEIS

%I #22 May 11 2026 09:22:25

%S 0,0,0,1,1,2,2,3,4,5,7,9,12,15,20,25,32,40,51,63,79,98,121,149,184,

%T 224,274,334,405,490,593,713,858,1029,1231,1470,1754,2084,2476,2935,

%U 3473,4101,4839,5695,6698,7862,9216,10787,12614,14721,17167,19989,23249,27004,31337,36313

%N Number of rectangular plane partitions of n with exactly 2 rows and with rows and columns strictly decreasing.

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

%e The a(10) = 7 matrices:

%e   [9] [8] [7] [6] [5 2] [4 2] [4 3]

%e   [1] [2] [3] [4] [2 1] [3 1] [2 1]

%o (PARI) my(N=60, q='q+O('q^N)); concat([0, 0, 0], Vec(sum(k=1, N, q^(k*(k+2))*prod(i=1, 2, prod(j=1, k, 1/(1-q^(i+j-1)))))))

%Y Column k=2 of A394187.

%Y Cf. A323430, A395924.

%K nonn

%O 0,6

%A _Seiichi Manyama_, May 10 2026