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 A301841 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero. 13
 1, 2, 2, 4, 8, 4, 8, 25, 32, 8, 16, 81, 139, 128, 16, 32, 263, 678, 773, 512, 32, 64, 855, 3182, 5748, 4299, 2048, 64, 128, 2778, 15199, 39703, 48802, 23909, 8192, 128, 256, 9027, 72514, 281758, 496085, 414385, 132971, 32768, 256, 512, 29333, 346244 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ...1......2.......4.........8..........16...........32.............64 ...2......8......25........81.........263..........855...........2778 ...4.....32.....139.......678........3182........15199..........72514 ...8....128.....773......5748.......39703.......281758........1986213 ..16....512....4299.....48802......496085......5240684.......54948498 ..32...2048...23909....414385.....6196305.....97439921.....1518341751 ..64...8192..132971...3518619....77396422...1812097252....41966406867 .128..32768..739525..29877293...966770632..33701001773..1159968653556 .256.131072.4112907.253694309.12076215811.626769301255.32062561937804 LINKS R. H. Hardin, Table of n, a(n) for n = 1..417 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) -8*a(n-2) for n>3 k=4: a(n) = 13*a(n-1) -46*a(n-2) +72*a(n-3) -57*a(n-4) +16*a(n-5) for n>6 k=5: [order 11] for n>13 k=6: [order 25] for n>27 k=7: [order 53] for n>56 Empirical for row n: n=1: a(n) = 2*a(n-1) n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6 n=3: [order 12] for n>14 n=4: [order 35] for n>38 n=5: [order 99] for n>104 EXAMPLE Some solutions for n=5 k=4 ..0..1..1..0. .0..1..0..1. .0..1..1..1. .0..0..0..0. .0..0..1..1 ..1..0..1..0. .1..1..0..1. .1..0..1..0. .1..1..0..1. .0..1..0..1 ..1..0..1..1. .1..0..1..0. .1..0..1..1. .0..1..0..1. .1..1..0..1 ..0..1..0..0. .0..0..1..0. .1..0..1..1. .0..0..1..0. .0..1..0..0 ..1..0..1..0. .0..1..0..1. .1..0..0..0. .1..1..0..1. .1..1..1..1 CROSSREFS Column 1 is A000079(n-1). Column 2 is A004171(n-1). Row 1 is A000079(n-1). Sequence in context: A299359 A299180 A299942 * A302069 A298195 A299089 Adjacent sequences:  A301838 A301839 A301840 * A301842 A301843 A301844 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 27 2018 STATUS approved

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Last modified January 25 17:35 EST 2022. Contains 350572 sequences. (Running on oeis4.)