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%I #4 Jan 02 2015 19:33:09
%S 81,414,414,1388,1377,1388,3639,3090,2640,3639,8501,5386,4196,4720,
%T 8501,19701,9679,6476,6931,9654,19701,48293,20975,11937,10477,13528,
%U 22236,48293,126357,51167,25715,18526,19475,29370,55362,126357,346997,133311
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally
%C Table starts
%C .....81.....414....1388....3639....8501...19701...48293..126357...346997
%C ....414....1377....3090....5386....9679...20975...51167..133311...362399
%C ...1388....2640....4196....6476...11937...25715...60586..151946...399466
%C ...3639....4720....6931...10477...18526...37469...82676..194708...483572
%C ...8501....9654...13528...19475...32652...61955..127898..281402...653210
%C ..19701...22236...29370...40117...63550..113573..220988..457436...995132
%C ..48293...55362...68992...89339..133284..224747..415106..817442..1686914
%C .126357..145428..172050..211597..296566..470909..827156.1561268..3094292
%C .346997..397002..449608..527555..694572.1034675.1722698.3120362..5980490
%C .982677.1114476.1219050.1373797.1704910.2376533.3728108.6452876.11967212
%H R. H. Hardin, <a href="/A253495/b253495.txt">Table of n, a(n) for n = 1..362</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>10
%F k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>8
%F k=3: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>7
%F k=4: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>6
%F k=5: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>6
%F k=6: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>6
%F k=7: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>6
%F Empirical for row n:
%F n=1: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>10
%F n=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9
%F n=3: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9
%F n=4: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9
%F n=5: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9
%F n=6: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9
%F n=7: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9
%F Empirical for column k:
%F k=1: a(n) = 400*3^(n-3) + 205*2^(n-1) + 2917 for n>7
%F k=2: a(n) = 49*3^(n-1) + 291*2^(n-1) + 1017 for n>5
%F k=3: a(n) = 49*3^(n-1) + 494*2^(n-1) + 1655 for n>4
%F k=4: a(n) = 49*3^(n-1) + 794*2^(n-1) + 2802 for n>3
%F k=5: a(n) = 49*3^(n-1) + 1435*2^(n-1) + 5723 for n>3
%F k=6: a(n) = 49*3^(n-1) + 2730*2^(n-1) + 14306 for n>3
%F k=7: a(n) = 49*3^(n-1) + 5322*2^(n-1) + 38777 for n>3
%F k=8: a(n) = 49*3^(n-1) + 10506*2^(n-1) + 109337 for n>3
%F k=9: a(n) = 49*3^(n-1) + 20874*2^(n-1) + 315257 for n>3
%F Empirical for row n:
%F n=1: a(n) = 400*3^(n-3) + 205*2^(n-1) + 2917 for n>7
%F n=2: a(n) = 400*3^(n-3) + 271*2^(n-1) + 1423 for n>6
%F n=3: a(n) = 400*3^(n-3) + 415*2^(n-1) + 1626 for n>6
%F n=4: a(n) = 400*3^(n-3) + 738*2^(n-1) + 3044 for n>6
%F n=5: a(n) = 400*3^(n-3) + 1386*2^(n-1) + 6794 for n>6
%F n=6: a(n) = 400*3^(n-3) + 2682*2^(n-1) + 16940 for n>6
%F n=7: a(n) = 400*3^(n-3) + 5274*2^(n-1) + 45170 for n>6
%F n=8: a(n) = 400*3^(n-3) + 10458*2^(n-1) + 125444 for n>6
%F n=9: a(n) = 400*3^(n-3) + 20826*2^(n-1) + 357434 for n>6
%e Some solutions for n=4 k=4
%e ..1..1..2..1..1....0..2..2..2..2....0..0..2..1..1....0..2..1..2..1
%e ..1..0..1..0..0....1..0..0..0..0....1..0..1..0..0....1..2..1..2..1
%e ..1..0..1..0..0....2..1..1..1..1....2..1..2..1..1....0..1..0..1..0
%e ..2..1..2..1..1....1..0..0..0..0....2..1..2..1..1....0..1..0..1..0
%e ..1..0..1..0..2....1..0..0..1..2....1..0..1..0..0....0..1..0..2..2
%Y Column 1 and row 1 are A253449
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 02 2015
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