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A223918 T(n,k)=Number of nXk 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A223918 #6 Jul 23 2025 04:38:59
%S A223918 3,9,6,22,36,10,46,158,100,15,86,548,666,225,21,148,1600,3311,2111,
%T A223918 441,28,239,4102,13347,14123,5548,784,36,367,9503,45988,74040,48182,
%U A223918 12752,1296,45,541,20299,140236,323394,319156,139925,26494,2025,55,771,40570
%N A223918 T(n,k)=Number of nXk 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A223918 Table starts
%C A223918 ..3....9.....22......46.......86.......148........239.........367..........541
%C A223918 ..6...36....158.....548.....1600......4102.......9503.......20299........40570
%C A223918 .10..100....666....3311....13347.....45988.....140236......387671.......988447
%C A223918 .15..225...2111...14123....74040....323394....1226491.....4157102.....12856218
%C A223918 .21..441...5548...48182...319156...1721356....7906972....31947798....116289938
%C A223918 .28..784..12752..139925..1147712...7526024...41334135...196691651....831996762
%C A223918 .36.1296..26494..359344..3588729..28247478..183720802..1022160764...4994941017
%C A223918 .45.2025..50863..837243.10031780..93683295..715114500..4620831232..25961964085
%C A223918 .55.3025..91634.1802306.25574524.280338123.2489822632.18558764134.119279565646
%C A223918 .66.4356.156682.3633256.60357024.769012348.7881608430.67311575302.492221386729
%H A223918 R. H. Hardin, <a href="/A223918/b223918.txt">Table of n, a(n) for n = 1..480</a>
%F A223918 Empirical: columns k=1..7 are polynomials of degree 2*k for n>0,0,0,1,2,3,4
%F A223918 Empirical: rows n=1..7 are polynomials of degree 4*n
%e A223918 Some solutions for n=3 k=4
%e A223918 ..0..2..1..0....1..2..2..0....0..0..1..0....1..0..0..0....1..0..0..0
%e A223918 ..0..2..1..1....1..2..2..0....0..0..1..1....1..1..1..1....1..0..0..0
%e A223918 ..1..2..1..1....1..2..2..0....0..1..2..1....2..2..2..2....2..2..2..0
%Y A223918 Column 1 is A000217(n+1)
%Y A223918 Column 2 is A000537(n+1)
%Y A223918 Row 1 is A223718
%K A223918 nonn,tabl
%O A223918 1,1
%A A223918 _R. H. Hardin_ Mar 29 2013