A394348 - OEIS

%I #17 May 11 2026 09:22:12

%S 0,0,0,0,0,0,1,1,2,3,4,5,7,8,10,13,15,19,24,30,37,49,60,78,98,125,155,

%T 199,243,306,376,466,566,700,844,1033,1246,1513,1817,2203,2636,3180,

%U 3808,4575,5464,6557,7815,9347,11132,13274,15774,18773,22255,26409,31257,36986,43667,51557

%N Number of rectangular plane partitions of n with exactly 3 rows and with rows and columns strictly decreasing.

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

%e The a(10) = 4 matrices:

%e   [7] [6] [5] [5]

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

%e   [1] [1] [1] [2]

%o (PARI) my(N=60, q='q+O('q^N)); concat([0, 0, 0, 0, 0, 0], Vec(sum(k=1, N, q^(3*k*(k+3)/2)*prod(i=1, 3, prod(j=1, k, 1/(1-q^(i+j-1)))))))

%Y Column k=3 of A394187.

%Y Cf. A323430, A395925.

%K nonn

%O 0,9

%A _Seiichi Manyama_, May 10 2026