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%I #4 Feb 13 2015 10:52:45
%S 512,2554,2554,10732,9492,10732,42890,39935,33778,42890,154680,149676,
%T 100001,87907,154680,516998,470542,246173,154706,196724,516998,
%U 1640073,1327776,566341,281112,256941,407885,1640073,5004712,3504157,1217347
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock sum of the two sums of the central row and central column minus the two minimums of the diagonal and antidiagonal nondecreasing horizontally, vertically and ne-to-sw antidiagonally
%C Table starts
%C ......512....2554..10732..42890.154680..516998.1640073.5004712.14785630
%C .....2554....9492..39935.149676.470542.1327776.3504157.8592073.19523668
%C ....10732...33778.100001.246173.566341.1217347.2396285.4226143..7066617
%C ....42890...87907.154706.281112.474308..749830.1231466.1903222..3236146
%C ...154680..196724.256941.340084.509796..679364.1001108.1527986..2511384
%C ...516998..407885.346115.301745.427420..553864..819368.1126316..1771048
%C ..1640073..794663.425667.310872.427492..546968..813888.1126442..1716252
%C ..5004712.1460513.483327.321641.432916..587072..838084.1108752..1685408
%C .14785630.2583757.564619.365650.485356..613136..885048.1199594..1779292
%C .42521002.4473909.632901.388347.514932..661012..936028.1211228..1811032
%H R. H. Hardin, <a href="/A255036/b255036.txt">Table of n, a(n) for n = 1..2114</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 21] for n>27
%F k=2: [order 36] for n>42
%F k=3: [order 12] for n>23
%F k=4: [same order 12] for n>20
%F k=5: [same order 12] for n>20
%F k=6: [same order 12] for n>21
%F k=7: [same order 12] for n>20
%F Empirical for row n:
%F n=1: [same linear recurrence of order 21] for n>27
%F n=2: [order 50] for n>63
%F n=3: [order 29] for n>47
%F n=4: [order 22] for n>38
%F n=5: [order 17] for n>33
%F n=6: [same order 17] for n>34
%F n=7: [same order 17] for n>36
%e Some solutions for n=3 k=4
%e ..1..0..1..1..0..0....1..0..1..0..0..0....1..0..0..0..0..0....1..0..1..0..0..1
%e ..1..0..0..0..0..0....0..0..0..0..0..1....0..0..0..0..0..1....0..1..0..0..1..1
%e ..0..0..0..0..1..0....0..0..0..1..0..1....0..0..0..0..0..0....1..0..0..1..1..0
%e ..0..1..1..1..1..1....1..1..0..1..1..1....0..0..0..1..1..0....0..0..1..1..1..1
%e ..1..1..0..0..0..1....1..0..1..0..0..0....0..0..1..1..1..0....1..1..1..0..0..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 13 2015
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