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 A281469 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards. 13
 1, 2, 2, 4, 8, 4, 8, 17, 25, 8, 16, 37, 24, 81, 16, 32, 78, 39, 60, 264, 32, 64, 169, 57, 96, 133, 857, 64, 128, 361, 87, 130, 207, 283, 2785, 128, 256, 778, 145, 176, 278, 405, 634, 9050, 256, 512, 1673, 241, 260, 358, 534, 897, 1419, 29407, 512, 1024, 3605, 397, 406 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ...1.....2....4....8....16....32....64...128...256...512..1024..2048..4096 ...2.....8...17...37....78...169...361...778..1673..3605..7774.16777.36241 ...4....25...24...39....57....87...145...241...397...669..1133..1909..3229 ...8....81...60...96...130...176...260...406...636...996..1586..2552..4108 ..16...264..133..207...278...358...472...658...974..1476..2246..3446..5334 ..32...857..283..405...534...706...924..1190..1602..2290..3374..5036..7604 ..64..2785..634..897..1106..1422..1887..2429..3093..4063..5629..8037.11711 .128..9050.1419.1975..2362..2858..3681..4795..6109..7699..9985.13483.18797 .256.29407.3092.4154..4901..5793..7126..9058.11794.14920.18660.23832.31694 .512.95557.6849.8884.10240.11986.14363.17511.22411.28951.36521.45125.56983 LINKS R. H. Hardin, Table of n, a(n) for n = 1..481 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) k=3: a(n) = 2*a(n-1) +3*a(n-3) -3*a(n-4) -4*a(n-5) +4*a(n-6) -4*a(n-7) for n>9 k=4: a(n) = a(n-1) +a(n-2) +4*a(n-3) +a(n-4) -4*a(n-5) -5*a(n-6) +3*a(n-8) for n>10 k=5: [order 10] for n>15 k=6: [order 11] for n>17 k=7: [order 12] for n>19 Empirical for row n: n=1: a(n) = 2*a(n-1) n=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) -2*a(n-4) +4*a(n-5) for n>6 n=3: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -2*a(n-4) for n>8 n=4: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -a(n-5) for n>9 n=5: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -a(n-4) +a(n-5) -a(n-6) for n>11 n=6: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -a(n-4) +a(n-6) -a(n-7) for n>12 n=7: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -a(n-4) +a(n-7) -a(n-8) for n>16 EXAMPLE Some solutions for n=4 k=4 ..0..1..0..0. .0..1..0..1. .0..0..1..0. .0..1..0..1. .0..1..1..0 ..1..1..0..1. .0..1..0..1. .1..1..0..1. .0..1..0..1. .0..1..0..0 ..1..0..0..1. .1..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1 ..1..0..1..1. .1..0..0..0. .1..1..0..1. .1..0..1..0. .1..1..0..1 CROSSREFS Column 1 is A000079(n-1). Column 2 is A240478. Row 1 is A000079(n-1). Sequence in context: A121175 A183397 A339490 * A302623 A302415 A303182 Adjacent sequences: A281466 A281467 A281468 * A281470 A281471 A281472 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Jan 22 2017 STATUS approved

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Last modified December 2 10:01 EST 2022. Contains 358493 sequences. (Running on oeis4.)