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A223933 T(n,k)=Number of nXk 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

%I A223933 #6 Jul 23 2025 04:40:04
%S A223933 3,9,9,22,54,22,46,218,218,46,86,698,1116,698,86,148,1915,4498,4498,
%T A223933 1915,148,239,4690,15791,21334,15791,4690,239,367,10511,49646,86439,
%U A223933 86439,49646,10511,367,541,21919,142177,316136,386495,316136,142177,21919,541
%N A223933 T(n,k)=Number of nXk 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.
%C A223933 Table starts
%C A223933 ...3.....9......22.......46........86........148........239.........367
%C A223933 ...9....54.....218......698......1915.......4690......10511.......21919
%C A223933 ..22...218....1116.....4498.....15791......49646.....142177......375777
%C A223933 ..46...698....4498....21334.....86439.....316136....1065625.....3337831
%C A223933 ..86..1915...15791....86439....386495....1548633....5773556....20277077
%C A223933 .148..4690...49646...316136...1548633....6621074...26250443....98910688
%C A223933 .239.10511..142177..1065625...5773556...26250443..108796955...427868778
%C A223933 .367.21919..375777..3337831..20277077...98910688..427868778..1735753333
%C A223933 .541.43045..926559..9773219..67308910..356869229.1623374603..6788778441
%C A223933 .771.80334.2150622.26903878.211460339.1233491661.5968786086.25890527027
%H A223933 R. H. Hardin, <a href="/A223933/b223933.txt">Table of n, a(n) for n = 1..180</a>
%F A223933 Empirical: columns k=1..6 are polynomials of degree 4*k for n>0,0,3,6,9,12
%e A223933 Some solutions for n=3 k=4
%e A223933 ..0..0..2..1....0..0..0..1....0..1..1..2....2..2..2..2....1..1..0..0
%e A223933 ..0..1..1..2....0..2..1..1....0..0..2..2....1..2..2..2....1..1..1..2
%e A223933 ..0..1..1..2....0..2..2..2....0..0..2..2....1..2..2..2....0..1..2..1
%Y A223933 Column 1 is A223718
%K A223933 nonn,tabl
%O A223933 1,1
%A A223933 _R. H. Hardin_ Mar 29 2013