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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
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
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: A359488 A183397 A339490 * A302623 A302415 A303182
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 22 2017
STATUS
approved