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 A297374 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0, 1 or 2 neighboring 1s. 13
 2, 4, 4, 8, 16, 8, 16, 57, 64, 16, 32, 208, 393, 256, 32, 64, 765, 2610, 2719, 1024, 64, 128, 2807, 17534, 33054, 18805, 4096, 128, 256, 10294, 116932, 409507, 418344, 130063, 16384, 256, 512, 37759, 780273, 4986469, 9554038, 5294713, 899565, 65536, 512 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ...2......4........8..........16............32..............64 ...4.....16.......57.........208...........765............2807 ...8.....64......393........2610.........17534..........116932 ..16....256.....2719.......33054........409507.........4986469 ..32...1024....18805......418344.......9554038.......211988289 ..64...4096...130063.....5294713.....222925151......9012089653 .128..16384...899565....67012245....5201484239....383128155296 .256..65536..6221735...848136217..121365562862..16287817972455 .512.262144.43031893.10734382366.2831807366510.692439110062325 LINKS R. H. Hardin, Table of n, a(n) for n = 1..541 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) k=2: a(n) = 4*a(n-1) k=3: a(n) = 7*a(n-1) -4*a(n-3) k=4: a(n) = 13*a(n-1) -4*a(n-2) -3*a(n-3) -19*a(n-4) +15*a(n-5) -a(n-6) k=5: [order 9] for n>11 k=6: [order 17] for n>19 k=7: [order 28] for n>31 Empirical for row n: n=1: a(n) = 2*a(n-1) n=2: a(n) = 3*a(n-1) +a(n-2) +5*a(n-3) +a(n-4) +a(n-5) -a(n-6) -a(n-7) n=3: [order 12] for n>14 n=4: [order 29] for n>31 n=5: [order 84] for n>87 EXAMPLE Some solutions for n=5 k=4 ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..0 ..1..0..1..0. .1..0..0..1. .0..0..0..0. .0..1..0..0. .0..0..0..0 ..1..0..1..0. .1..0..0..1. .1..0..0..1. .1..0..1..1. .0..1..1..1 ..1..0..0..0. .1..0..0..1. .0..1..0..0. .1..0..1..1. .0..0..1..0 ..0..0..0..0. .0..0..1..1. .0..1..0..0. .1..0..0..1. .0..0..1..1 CROSSREFS Column 1 is A000079. Column 2 is A000302. Row 1 is A000079. Sequence in context: A283130 A295716 A282399 * A297102 A283415 A283857 Adjacent sequences:  A297371 A297372 A297373 * A297375 A297376 A297377 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Dec 29 2017 STATUS approved

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Last modified January 24 10:22 EST 2020. Contains 331193 sequences. (Running on oeis4.)