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%I #6 Jan 11 2015 11:05:37
%S 81,450,450,1998,2723,1998,7803,10182,16625,7803,28107,29737,77414,
%T 75959,28107,95940,70590,247252,382973,305707,95940,315576,148134,
%U 583698,1143174,1636717,1087364,315576,1011357,298760,1204422,2351928,5195288
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically
%C Table starts
%C ......81......450......1998......7803......28107......95940.....315576
%C .....450.....2723.....10182.....29737......70590.....148134.....298760
%C ....1998....16625.....77414....247252.....583698....1204422....2363797
%C ....7803....75959....382973...1143174....2351928....4249381....7348144
%C ...28107...305707...1636717...5195288...10966149...19685575...33767784
%C ...95940..1087364...5648005..17656505...36766701...64166071..106040628
%C ..315576..3598487..17980643..54890203..112645903..199063466..333213583
%C .1011357.11219006..52078415.150904540..295452432..515093745..871426149
%C .3181653.33417573.140931619.390365827..734787935.1244615026.2111246736
%C .9876870.95950526.357840627.928677156.1658583509.2727201405.4561812863
%H R. H. Hardin, <a href="/A253749/b253749.txt">Table of n, a(n) for n = 1..571</a>
%F Empirical for column k:
%F k=1: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)
%F k=2: [order 42] for n>46
%F k=3: [order 35] for n>45
%F k=4: [order 35] for n>47
%F k=5: [order 26] for n>41
%F k=6: [same order 26] for n>40
%F k=7: [same order 26] for n>41
%F Empirical for row n:
%F n=1: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)
%F n=2: [order 19] for n>25
%F n=3: [order 23] for n>30
%F n=4: [order 19] for n>27
%F n=5: [same order 19] for n>28
%F n=6: [same order 19] for n>29
%F n=7: [same order 19] for n>30
%F Empirical quasipolynomials for column k:
%F k=5: polynomial of degree 10 plus a quasipolynomial of degree 4 with period 4 for n>15
%F k=6: polynomial of degree 10 plus a quasipolynomial of degree 4 with period 4 for n>14
%F k=7: polynomial of degree 10 plus a quasipolynomial of degree 4 with period 4 for n>15
%F Empirical quasipolynomials for row n:
%F n=4: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>8
%F n=5: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>9
%F n=6: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>10
%F n=7: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>11
%e Some solutions for n=3 k=4
%e ..0..1..0..0..1....0..0..0..0..1....0..1..1..1..2....0..0..0..1..1
%e ..2..1..0..0..0....2..1..0..0..1....1..0..0..0..1....1..0..0..0..0
%e ..2..1..0..0..1....2..1..1..0..1....2..2..2..2..2....2..2..2..2..2
%e ..2..1..0..0..1....2..2..1..1..1....2..1..1..0..2....1..1..1..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 11 2015
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