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%I #4 Jun 01 2015 13:35:22
%S 512,2371,2371,6516,7334,6516,16196,13616,13616,16196,47704,23785,
%T 19920,23785,47704,156873,45771,25076,25076,45771,156873,488240,91023,
%U 25532,18282,25532,91023,488240,1356489,169230,23907,9784,9784,23907,169230
%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 diagonal and antidiagonal minus the two sums of the central column and central row nondecreasing horizontally and vertically
%C Table starts
%C ......512....2371..6516.16196.47704.156873.488240.1356489.3595084.9838222
%C .....2371....7334.13616.23785.45771..91023.169230..300889..536665..960950
%C .....6516...13616.19920.25076.25532..23907..23398...26321...30168...33303
%C ....16196...23785.25076.18282..9784...5331...3904....3384....2918....2518
%C ....47704...45771.25532..9784..4028...2176...1362.....994....1054.....915
%C ...156873...91023.23907..5331..2176...1256....767.....588.....649.....530
%C ...488240..169230.23398..3904..1362....767....520.....442.....396.....388
%C ..1356489..300889.26321..3384...994....588....442.....424.....348.....336
%C ..3595084..536665.30168..2918..1054....649....396.....348.....312.....310
%C ..9838222..960950.33303..2518...915....530....388.....336.....310.....252
%C .27777116.1692043.35726..2590...948....541....354.....300.....306.....246
%C .77335445.2898384.37801..2760...954....519....332.....282.....268.....228
%H R. H. Hardin, <a href="/A258522/b258522.txt">Table of n, a(n) for n = 1..7562</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 30] for n>34
%F k=2: [order 94] for n>105
%F k=3: [order 19] for n>39
%F k=4: a(n) = -a(n-1) -a(n-2) -a(n-3) +a(n-5) +a(n-6) +a(n-7) +a(n-8) for n>19
%F k=5: a(n) = -a(n-1) -a(n-2) -a(n-3) +a(n-5) +a(n-6) +a(n-7) +a(n-8) for n>19
%F k=6: a(n) = a(n-5) for n>16
%F k=7: a(n) = -a(n-2) +a(n-5) +a(n-7) for n>18
%F Empirical periods for column k:
%F k=4: period 20 starting at n=12: 2760 2878 2779 2550 2508 2654 2902 2899 2512 2402 2678 3022 2861 2406 2426 2798 2984 2755 2430 2546
%F k=5: period 20 starting at n=12: 954 844 1017 896 934 918 869 1028 896 898 943 880 1028 860 923 954 880 992 885 934
%F k=6: period 5 starting at n=12: 519 486 567 482 521
%F k=7: period 20 starting at n=12: 332 348 316 340 336 336 344 312 344 340 332 340 316 348 336 328 344 320 344 332
%e Some solutions for n=4 k=4
%e ..1..1..1..1..1..0....1..1..0..0..0..1....0..1..0..0..0..0....0..1..0..0..0..1
%e ..1..0..1..1..1..0....0..0..1..0..1..1....1..0..0..1..1..0....1..1..0..0..1..1
%e ..1..1..1..0..0..1....0..0..1..0..1..1....1..1..1..0..0..1....0..0..1..1..1..0
%e ..1..1..0..0..0..1....0..0..0..1..1..1....1..1..1..0..0..1....0..1..1..0..0..1
%e ..0..0..0..1..0..0....0..1..0..1..0..1....1..0..0..1..1..0....0..0..0..1..1..1
%e ..1..1..1..1..1..1....0..1..1..1..0..1....0..1..1..1..0..1....0..1..1..1..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jun 01 2015
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