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A224057 T(n,k)=Number of nXk 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing.

%I A224057 #6 Jul 23 2025 04:58:40
%S A224057 3,9,9,22,54,22,46,218,218,46,86,698,1232,698,86,148,1915,5219,5219,
%T A224057 1915,148,239,4690,18502,27246,18502,4690,239,367,10511,57911,115716,
%U A224057 115716,57911,10511,367,541,21919,164781,428949,568107,428949,164781,21919,541
%N A224057 T(n,k)=Number of nXk 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing.
%C A224057 Table starts
%C A224057 ...3.....9......22.......46........86........148.........239.........367
%C A224057 ...9....54.....218......698......1915.......4690.......10511.......21919
%C A224057 ..22...218....1232.....5219.....18502......57911......164781......433762
%C A224057 ..46...698....5219....27246....115716.....428949.....1442005.....4492529
%C A224057 ..86..1915...18502...115716....568107....2392915.....9064541....31777144
%C A224057 .148..4690...57911...428949...2392915...11231300....46853641...179545949
%C A224057 .239.10511..164781..1442005...9064541...46853641...212819499...880290006
%C A224057 .367.21919..433762..4492529..31777144..179545949...880290006..3903149379
%C A224057 .541.43045.1068664.13133871.104876598..646161612..3395883003.16032541293
%C A224057 .771.80334.2485274.36307595.329032264.2215310269.12434367863.62103561341
%H A224057 R. H. Hardin, <a href="/A224057/b224057.txt">Table of n, a(n) for n = 1..199</a>
%F A224057 Empirical: columns k=1..7 are polynomials of degree 4*k for n>0,0,1,3,5,7,9
%e A224057 Some solutions for n=3 k=4
%e A224057 ..0..0..0..1....2..2..1..0....0..0..0..0....1..1..0..0....0..1..0..0
%e A224057 ..1..1..1..0....2..2..1..0....2..0..0..0....1..2..0..0....1..2..0..0
%e A224057 ..1..2..1..0....2..2..0..0....2..1..1..1....2..2..2..1....2..2..0..0
%Y A224057 Column 1 is A223718
%Y A224057 Column 2 is A223927
%K A224057 nonn,tabl
%O A224057 1,1
%A A224057 _R. H. Hardin_ Mar 30 2013