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Number of 6 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
1

%I #6 Oct 18 2021 13:38:18

%S 7,49,232,824,2388,5992,13582,28642,57306,110164,205131,371923,658926,

%T 1143584,1947904,3261320,5374024,8725020,13970658,22081342,34476575,

%U 53211615,81232894,122724138,183570978,271978936,399288201,581038793

%N Number of 6 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%C Row 6 of A223838.

%H R. H. Hardin, <a href="/A223842/b223842.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/479001600)*n^12 - (1/15966720)*n^11 + (13/6220800)*n^10 - (1/53760)*n^9 + (6631/14515200)*n^8 + (125/96768)*n^7 - (1017767/43545600)*n^6 + (1429367/1451520)*n^5 - (7479853/1555200)*n^4 + (4300223/120960)*n^3 - (151629803/1663200)*n^2 - (12136/231)*n + 528 for n>6.

%e Some solutions for n=3

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

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

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

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

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

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

%Y Cf. A223838.

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 27 2013