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%I #5 Jan 02 2015 20:09:07
%S 132,260,260,428,472,428,636,784,784,636,884,1196,1332,1196,884,1172,
%T 1712,2088,2088,1712,1172,1500,2340,3052,3400,3052,2340,1500,1868,
%U 3088,4248,5136,5136,4248,3088,1868,2276,3964,5692,7396,7948,7396,5692,3964
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 2X2 and 3X3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically
%C Table starts
%C ..132..260...428...636...884..1172...1500...1868...2276...2724...3212...3740
%C ..260..472...784..1196..1712..2340...3088...3964...4976...6132...7440...8908
%C ..428..784..1332..2088..3052..4248...5692...7404...9404..11712..14348..17332
%C ..636.1196..2088..3400..5136..7396..10236..13748..18024..23168..29292..36516
%C ..884.1712..3052..5136..7948.11740..16592..22720..30300..39560..50740..64104
%C .1172.2340..4248..7396.11740.17888..25988..36632..50248..67508..89120.115940
%C .1500.3088..5692.10236.16592.25988..38564..55576..77680.106248.142556.188308
%C .1868.3964..7404.13748.22720.36632..55576..82200.117588.164828.226540.306780
%C .2276.4976..9404.18024.30300.50248..77680.117588.171236.244528.341444.469544
%C .2724.6132.11712.23168.39560.67508.106248.164828.244528.356736.507648.712368
%H R. H. Hardin, <a href="/A253510/b253510.txt">Table of n, a(n) for n = 1..9378</a>
%F Empirical for column k:
%F k=1: a(n) = 20*n^2 + 68*n + 44
%F k=2: a(n) = (4/3)*n^3 + 36*n^2 + (332/3)*n + 92 for n>2
%F k=3: a(n) = (10/3)*n^3 + 64*n^2 + (566/3)*n + 92 for n>4
%F k=4: a(n) = (1/3)*n^4 + 6*n^3 + (329/3)*n^2 + 288*n - 12 for n>6
%F k=5: a(n) = (5/6)*n^4 + 9*n^3 + (1135/6)*n^2 + 361*n - 300 for n>8
%F k=6: a(n) = (1/15)*n^5 + (4/3)*n^4 + (37/3)*n^3 + (1004/3)*n^2 + (1238/5)*n - 772 for n>10
%F k=7: a(n) = (1/6)*n^5 + (11/6)*n^4 + (97/6)*n^3 + (3661/6)*n^2 - (1501/3)*n - 980 for n>12
%e Some solutions for n=4 k=4
%e ..0..1..1..1..1..0....0..1..1..1..1..1....0..1..1..1..1..1....0..1..1..1..1..1
%e ..1..1..1..1..1..0....1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1
%e ..1..1..1..1..0..1....1..1..1..1..0..0....1..1..0..0..0..0....1..1..1..1..1..0
%e ..1..1..0..1..0..1....1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..0..0
%e ..1..1..0..1..0..1....1..1..0..0..0..0....1..0..0..0..0..0....1..1..1..1..1..1
%e ..1..0..0..1..0..1....1..1..1..1..1..1....0..1..1..1..1..1....0..0..0..0..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 02 2015