login
Number of 6 X 6 matrices with elements in 0..n with each row and each column in nondecreasing order. 6,6,n can be permuted, see formula.
0

%I #7 Jan 17 2025 09:28:47

%S 1,924,226512,24293412,1447482465,55197331332,1478619421136,

%T 29706808370096,469699956117392,6062460972064640,65728947490132992,

%U 612416828057104512,4995284546047230864,36217696550300209296,236405501218419838800,1404221840699607829900

%N Number of 6 X 6 matrices with elements in 0..n with each row and each column in nondecreasing order. 6,6,n can be permuted, see formula.

%H Feihu Liu, Guoce Xin, and Chen Zhang, <a href="https://arxiv.org/abs/2412.18744">Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS</a>, arXiv:2412.18744 [math.CO], 2024. See p. 25.

%F (empirical) set p,q,r to n,6,6 (in any order) in s=p+q+r-1; a(n) = product {i in 0..r-1} (binomial(s,p+i)*i!/(s-i)^(r-i-1))

%K nonn

%O 0,2

%A _R. H. Hardin_, Jul 05 2008