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A224391 T(n,k)=Number of nXk 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

%I A224391 #6 Jul 23 2025 05:09:01
%S A224391 4,10,16,20,100,64,35,400,1000,256,56,1225,6094,10000,1024,84,3136,
%T A224391 27790,86701,100000,4096,120,7056,102232,497958,1268572,1000000,16384,
%U A224391 165,14400,319769,2332222,8573507,18794636,10000000,65536,220,27225,881519
%N A224391 T(n,k)=Number of nXk 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.
%C A224391 Table starts
%C A224391 .......4..........10...........20.............35..............56
%C A224391 ......16.........100..........400...........1225............3136
%C A224391 ......64........1000.........6094..........27790..........102232
%C A224391 .....256.......10000........86701.........497958.........2332222
%C A224391 ....1024......100000......1268572........8573507........45648753
%C A224391 ....4096.....1000000.....18794636......152271025.......879830242
%C A224391 ...16384....10000000....279128617.....2780848289.....17642791909
%C A224391 ...65536...100000000...4142692993....51325449985....365858453951
%C A224391 ..262144..1000000000..61481903024...949582166068...7713944320142
%C A224391 .1048576.10000000000.912523782542.17572045403455.163629606236587
%H A224391 R. H. Hardin, <a href="/A224391/b224391.txt">Table of n, a(n) for n = 1..198</a>
%F A224391 Empirical for column k:
%F A224391 k=1: a(n) = 4*a(n-1)
%F A224391 k=2: a(n) = 10*a(n-1)
%F A224391 k=3: [order 15]
%F A224391 k=4: [order 47]
%F A224391 Empirical: rows n=1..6 are polynomials of degree 3*n for k>0,0,1,4,7,10
%e A224391 Some solutions for n=3 k=4
%e A224391 ..0..1..1..1....0..1..1..3....1..2..3..3....2..2..3..3....0..0..0..1
%e A224391 ..2..2..2..2....0..1..3..3....0..2..2..2....0..3..3..3....0..2..2..3
%e A224391 ..1..3..3..3....0..2..3..3....1..1..1..1....0..0..1..2....3..3..3..3
%Y A224391 Column 1 is A000302
%Y A224391 Column 2 is A011557
%Y A224391 Row 1 is A000292(n+1)
%Y A224391 Row 2 is A001249
%K A224391 nonn,tabl
%O A224391 1,1
%A A224391 _R. H. Hardin_ Apr 05 2013