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 A250783 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction 14
 9, 21, 18, 46, 46, 36, 99, 106, 96, 72, 209, 238, 230, 196, 144, 436, 518, 534, 482, 396, 288, 901, 1106, 1194, 1152, 990, 796, 576, 1849, 2326, 2604, 2640, 2426, 2010, 1596, 1152, 3774, 4838, 5568, 5882, 5688, 5028, 4054, 3196, 2304, 7671, 9978, 11732, 12796 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ....9....21....46....99....209....436.....901....1849....3774.....7671....15541 ...18....46...106...238....518...1106....2326....4838....9978....20446....41686 ...36....96...230...534...1194...2604....5568...11732...24442....50482...103566 ...72...196...482..1152...2640...5882...12796...27344...57610...120060...248072 ..144...396...990..2426...5688..12950...28692...62274..132890...279864...583196 ..288...796..2010..5028..12036..27986...63184..139436..301786...643164..1353544 ..576..1596..4054.10306..25126..59590..137082..307762..676266..1460260..3107536 .1152..3196..8146.20960..51904.125334..293588..670608.1496970..3278004..7061504 .2304..6396.16334.42394.106344.260916..621664.1444162.3275574..7278104.15884220 .4608.12796.32714.85420.216500.538538.1303276.3076788.7089558.15987988.35370676 LINKS R. H. Hardin, Table of n, a(n) for n = 1..544 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1); a(n) = 9*2^(n-1) k=2: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 25*2^(n-1) -4 k=3: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3) k=4: a(n) = 6*a(n-1) -14*a(n-2) +16*a(n-3) -9*a(n-4) +2*a(n-5) k=5: a(n) = 8*a(n-1) -27*a(n-2) +50*a(n-3) -55*a(n-4) +36*a(n-5) -13*a(n-6) +2*a(n-7) k=6: [order 9] k=7: [order 11] Empirical for row n: n=1: a(n) = 3*a(n-1) -a(n-2) -2*a(n-3) n=2: a(n) = 4*a(n-1) -4*a(n-2) -a(n-3) +2*a(n-4) n=3: a(n) = 5*a(n-1) -8*a(n-2) +3*a(n-3) +3*a(n-4) -2*a(n-5) n=4: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +11*a(n-4) -5*a(n-5) -3*a(n-6) +2*a(n-7) n=5: [order 8] n=6: [order 9] n=7: [order 10] EXAMPLE Some solutions for n=4 k=4 ..0..0..1..0..0....0..0..0..1..0....0..0..0..0..0....1..0..1..1..0 ..0..0..1..0..0....0..0..0..1..1....0..0..0..0..0....1..0..1..1..0 ..0..0..1..0..0....0..0..0..1..1....0..0..0..0..1....1..0..1..1..1 ..0..0..1..0..1....0..0..0..1..1....1..1..1..1..0....1..0..1..1..1 ..0..0..1..0..1....0..0..0..1..1....1..1..1..1..0....1..0..1..1..1 CROSSREFS Column 1 is A005010(n-1) Row 1 is A027973(n+1) Sequence in context: A157812 A218164 A161326 * A259250 A251219 A284131 Adjacent sequences:  A250780 A250781 A250782 * A250784 A250785 A250786 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Nov 27 2014 STATUS approved

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Last modified August 3 07:47 EDT 2021. Contains 346435 sequences. (Running on oeis4.)