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 A253495 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 14
 81, 414, 414, 1388, 1377, 1388, 3639, 3090, 2640, 3639, 8501, 5386, 4196, 4720, 8501, 19701, 9679, 6476, 6931, 9654, 19701, 48293, 20975, 11937, 10477, 13528, 22236, 48293, 126357, 51167, 25715, 18526, 19475, 29370, 55362, 126357, 346997, 133311 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts .....81.....414....1388....3639....8501...19701...48293..126357...346997 ....414....1377....3090....5386....9679...20975...51167..133311...362399 ...1388....2640....4196....6476...11937...25715...60586..151946...399466 ...3639....4720....6931...10477...18526...37469...82676..194708...483572 ...8501....9654...13528...19475...32652...61955..127898..281402...653210 ..19701...22236...29370...40117...63550..113573..220988..457436...995132 ..48293...55362...68992...89339..133284..224747..415106..817442..1686914 .126357..145428..172050..211597..296566..470909..827156.1561268..3094292 .346997..397002..449608..527555..694572.1034675.1722698.3120362..5980490 .982677.1114476.1219050.1373797.1704910.2376533.3728108.6452876.11967212 LINKS R. H. Hardin, Table of n, a(n) for n = 1..362 FORMULA Empirical for column k: k=1: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>10 k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>8 k=3: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>7 k=4: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>6 k=5: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>6 k=6: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>6 k=7: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>6 Empirical for row n: n=1: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>10 n=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9 n=3: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9 n=4: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9 n=5: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9 n=6: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9 n=7: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9 Empirical for column k: k=1: a(n) = 400*3^(n-3) + 205*2^(n-1) + 2917 for n>7 k=2: a(n) = 49*3^(n-1) + 291*2^(n-1) + 1017 for n>5 k=3: a(n) = 49*3^(n-1) + 494*2^(n-1) + 1655 for n>4 k=4: a(n) = 49*3^(n-1) + 794*2^(n-1) + 2802 for n>3 k=5: a(n) = 49*3^(n-1) + 1435*2^(n-1) + 5723 for n>3 k=6: a(n) = 49*3^(n-1) + 2730*2^(n-1) + 14306 for n>3 k=7: a(n) = 49*3^(n-1) + 5322*2^(n-1) + 38777 for n>3 k=8: a(n) = 49*3^(n-1) + 10506*2^(n-1) + 109337 for n>3 k=9: a(n) = 49*3^(n-1) + 20874*2^(n-1) + 315257 for n>3 Empirical for row n: n=1: a(n) = 400*3^(n-3) + 205*2^(n-1) + 2917 for n>7 n=2: a(n) = 400*3^(n-3) + 271*2^(n-1) + 1423 for n>6 n=3: a(n) = 400*3^(n-3) + 415*2^(n-1) + 1626 for n>6 n=4: a(n) = 400*3^(n-3) + 738*2^(n-1) + 3044 for n>6 n=5: a(n) = 400*3^(n-3) + 1386*2^(n-1) + 6794 for n>6 n=6: a(n) = 400*3^(n-3) + 2682*2^(n-1) + 16940 for n>6 n=7: a(n) = 400*3^(n-3) + 5274*2^(n-1) + 45170 for n>6 n=8: a(n) = 400*3^(n-3) + 10458*2^(n-1) + 125444 for n>6 n=9: a(n) = 400*3^(n-3) + 20826*2^(n-1) + 357434 for n>6 EXAMPLE Some solutions for n=4 k=4 ..1..1..2..1..1....0..2..2..2..2....0..0..2..1..1....0..2..1..2..1 ..1..0..1..0..0....1..0..0..0..0....1..0..1..0..0....1..2..1..2..1 ..1..0..1..0..0....2..1..1..1..1....2..1..2..1..1....0..1..0..1..0 ..2..1..2..1..1....1..0..0..0..0....2..1..2..1..1....0..1..0..1..0 ..1..0..1..0..2....1..0..0..1..2....1..0..1..0..0....0..1..0..2..2 CROSSREFS Column 1 and row 1 are A253449 Sequence in context: A237182 A237176 A102741 * A253456 A236155 A253449 Adjacent sequences:  A253492 A253493 A253494 * A253496 A253497 A253498 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Jan 02 2015 STATUS approved

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Last modified September 20 10:51 EDT 2021. Contains 347584 sequences. (Running on oeis4.)