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A280604
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T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
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8
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1, 2, 2, 4, 7, 4, 8, 18, 18, 8, 16, 50, 45, 50, 16, 32, 138, 116, 116, 138, 32, 64, 383, 293, 302, 293, 383, 64, 128, 1063, 735, 726, 726, 735, 1063, 128, 256, 2951, 1844, 1709, 1648, 1709, 1844, 2951, 256, 512, 8193, 4626, 3996, 3647, 3647, 3996, 4626, 8193, 512
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OFFSET
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1,2
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COMMENTS
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Table starts
...1.....2.....4.....8....16.....32.....64....128....256.....512....1024
...2.....7....18....50...138....383...1063...2951...8193...22748...63161
...4....18....45...116...293....735...1844...4626..11611...29151...73200
...8....50...116...302...726...1709...3996...9346..21891...51367..120680
..16...138...293...726..1648...3647...8031..17745..39427...87996..197061
..32...383...735..1709..3647...7594..15792..33136..70293..150510..324417
..64..1063..1844..3996..8031..15792..31152..62349.126893..261994..546766
.128..2951..4626..9346.17745..33136..62349.119656.234789..469715..953647
.256..8193.11611.21891.39427..70293.126893.234789.446500..869877.1726530
.512.22748.29151.51367.87996.150510.261994.469715.869877.1658080.3232058
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2) +a(n-3) +a(n-4) -2*a(n-5) -a(n-6)
k=3: a(n) = 4*a(n-1) -3*a(n-2) -3*a(n-3) +2*a(n-4) +3*a(n-5) -2*a(n-6) for n>8
k=4: a(n) = 4*a(n-1) -4*a(n-2) +2*a(n-5) -3*a(n-7) +2*a(n-8) +a(n-9) -a(n-10) for n>13
k=5: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) +2*a(n-6) -2*a(n-7) -3*a(n-8) +5*a(n-9) -a(n-10) -a(n-11) -a(n-12) +a(n-13) for n>15
k=6: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) +2*a(n-7) -2*a(n-8) -3*a(n-9) +5*a(n-10) -a(n-11) -a(n-12) -a(n-14) +a(n-15) for n>19
k=7: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) +2*a(n-8) -2*a(n-9) -3*a(n-10) +5*a(n-11) -a(n-12) -a(n-13) -a(n-16) +a(n-17) for n>22
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..0. .0..1..0..0. .0..1..1..1. .0..1..0..0. .0..1..0..1
..1..0..1..0. .1..0..1..0. .0..0..0..0. .1..0..1..0. .0..1..0..1
..1..0..1..0. .0..1..0..1. .1..1..1..0. .1..1..0..1. .0..1..0..0
..1..1..0..1. .0..0..1..0. .0..0..0..1. .0..0..1..1. .0..1..1..1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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