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 A253435 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally 14
 16, 39, 39, 69, 58, 69, 109, 70, 73, 109, 181, 102, 85, 108, 181, 325, 174, 120, 121, 180, 325, 613, 318, 192, 156, 193, 324, 613, 1189, 606, 336, 228, 228, 337, 612, 1189, 2341, 1182, 624, 372, 300, 372, 625, 1188, 2341, 4645, 2334, 1200, 660, 444, 444, 660, 1201 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ...16...39...69..109..181..325..613.1189.2341.4645..9253.18469.36901.73765 ...39...58...70..102..174..318..606.1182.2334.4638..9246.18462.36894.73758 ...69...73...85..120..192..336..624.1200.2352.4656..9264.18480.36912.73776 ..109..108..121..156..228..372..660.1236.2388.4692..9300.18516.36948.73812 ..181..180..193..228..300..444..732.1308.2460.4764..9372.18588.37020.73884 ..325..324..337..372..444..588..876.1452.2604.4908..9516.18732.37164.74028 ..613..612..625..660..732..876.1164.1740.2892.5196..9804.19020.37452.74316 .1189.1188.1201.1236.1308.1452.1740.2316.3468.5772.10380.19596.38028.74892 .2341.2340.2353.2388.2460.2604.2892.3468.4620.6924.11532.20748.39180.76044 .4645.4644.4657.4692.4764.4908.5196.5772.6924.9228.13836.23052.41484.78348 LINKS R. H. Hardin, Table of n, a(n) for n = 1..1101 FORMULA Empirical for diagonal: diagonal: a(n) = 3*a(n-1) -2*a(n-2) for n>5 Empirical for column k: k=1: a(n) = 3*a(n-1) -2*a(n-2) for n>5 k=2: a(n) = 3*a(n-1) -2*a(n-2) for n>5 k=3: a(n) = 3*a(n-1) -2*a(n-2) for n>4 k=4: a(n) = 3*a(n-1) -2*a(n-2) for n>3 k=5: a(n) = 3*a(n-1) -2*a(n-2) for n>3 k=6: a(n) = 3*a(n-1) -2*a(n-2) for n>3 k=7: a(n) = 3*a(n-1) -2*a(n-2) for n>3 Empirical for row n: n=1: a(n) = 3*a(n-1) -2*a(n-2) for n>5 n=2: a(n) = 3*a(n-1) -2*a(n-2) for n>5 n=3: a(n) = 3*a(n-1) -2*a(n-2) for n>5 n=4: a(n) = 3*a(n-1) -2*a(n-2) for n>5 n=5: a(n) = 3*a(n-1) -2*a(n-2) for n>5 n=6: a(n) = 3*a(n-1) -2*a(n-2) for n>5 n=7: a(n) = 3*a(n-1) -2*a(n-2) for n>5 Empirical for diagonal: diagonal: 9*2^n + 12 for n>3 Empirical for columns: k=1: 9*2^(n-1) + 37 for n>3 k=2: 9*2^(n-1) + 36 for n>3 k=3: 9*2^(n-1) + 49 for n>2 k=4: 9*2^(n-1) + 84 for n>1 k=5: 9*2^(n-1) + 156 for n>1 k=6: 9*2^(n-1) + 300 for n>1 k=7: 9*2^(n-1) + 588 for n>1 Empirical for rows: n=1: 9*2^(k-1) + 37 for k>3 n=2: 9*2^(k-1) + 30 for k>3 n=3: 9*2^(k-1) + 48 for k>3 n=4: 9*2^(k-1) + 84 for k>3 n=5: 9*2^(k-1) + 156 for k>3 n=6: 9*2^(k-1) + 300 for k>3 n=7: 9*2^(k-1) + 588 for k>3 Empirical: T(n,k) = 9*2(n-1) + 9*2^(k-1) + c, where rows n=1 c=28 for k>3 n>1 c=12 for k>3 columns k=1 c=28 for n>3 k=2 c=18 for n>3 k=3 c=13 for n>2 k>3 c=12 for n>1 summary table of c ..-2..12..24..28..28..28..28..28..28..28 ..12..22..16..12..12..12..12..12..12..12 ..24..19..13..12..12..12..12..12..12..12 ..28..18..13..12..12..12..12..12..12..12 ..28..18..13..12..12..12..12..12..12..12 ..28..18..13..12..12..12..12..12..12..12 ..28..18..13..12..12..12..12..12..12..12 ..28..18..13..12..12..12..12..12..12..12 ..28..18..13..12..12..12..12..12..12..12 ..28..18..13..12..12..12..12..12..12..12 EXAMPLE Some solutions for n=4 k=4 ..1..0..0..0..1....1..1..1..1..1....1..1..1..0..0....0..0..0..0..0 ..1..0..0..0..1....1..1..1..1..1....1..1..1..0..0....1..1..1..1..1 ..1..0..0..0..1....1..1..1..1..1....1..1..1..0..0....1..1..1..1..1 ..1..0..0..0..1....0..0..0..0..0....1..1..1..0..0....0..0..0..0..0 ..1..0..0..0..1....0..0..0..0..0....1..1..1..0..0....1..1..1..1..1 CROSSREFS Column 1 and row 1 are A253152 Sequence in context: A122029 A218900 A070585 * A253159 A308311 A121375 Adjacent sequences:  A253432 A253433 A253434 * A253436 A253437 A253438 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Dec 31 2014 STATUS approved

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Last modified December 8 11:17 EST 2021. Contains 349594 sequences. (Running on oeis4.)