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Number of nX6 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing
1

%I #4 Mar 27 2013 04:56:09

%S 22,169,607,1601,3699,8007,16742,34096,67890,132115,251110,465910,

%T 843960,1493505,2584666,4379914,7277630,11873716,19047873,30083272,

%U 46831011,71934087,109129744,163654129,242779358,356520541,518559236,747440414

%N Number of nX6 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing

%C Column 6 of A223770

%H R. H. Hardin, <a href="/A223768/b223768.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/479001600)*n^12 - (1/15966720)*n^11 + (23/8709120)*n^10 - (59/1451520)*n^9 + (22591/14515200)*n^8 - (1159/53760)*n^7 + (713737/1741824)*n^6 - (1665749/290304)*n^5 + (795178259/10886400)*n^4 - (220668799/362880)*n^3 + (73774259/20790)*n^2 - (340682581/27720)*n + 20228 for n>8

%e Some solutions for n=3

%e ..0..1..0..0..0..0....1..0..0..0..0..0....0..1..0..0..0..0....0..1..1..1..1..0

%e ..1..1..1..1..0..0....1..1..1..0..0..0....0..1..1..1..0..0....0..1..1..1..1..1

%e ..0..1..1..1..1..1....0..1..1..1..1..0....1..1..1..1..1..1....0..0..1..1..1..1

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 27 2013