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A302528
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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12
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0, 1, 0, 1, 3, 0, 2, 7, 10, 0, 3, 10, 28, 23, 0, 5, 27, 42, 115, 61, 0, 8, 45, 100, 168, 497, 162, 0, 13, 98, 290, 539, 902, 2086, 421, 0, 21, 193, 730, 1977, 3683, 3256, 9091, 1103, 0, 34, 379, 1700, 5942, 23909, 17546, 15852, 40575, 2890, 0, 55, 778, 4246, 16733, 128242
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OFFSET
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1,5
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COMMENTS
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Table starts
.0....1......1......2.......3.........5..........8..........13...........21
.0....3......7.....10......27........45.........98.........193..........379
.0...10.....28.....42.....100.......290........730........1700.........4246
.0...23....115....168.....539......1977.......5942.......16733........49219
.0...61....497....902....3683.....23909.....128242......465323......1918153
.0..162...2086...3256...17546....182773....1275348.....5557469.....29725028
.0..421...9091..15852...92603...1551340...16130212....82774516....506265517
.0.1103..40575..77904..615351..18089458..303355178..1916999716..16636194027
.0.2890.172996.314276.3268978.155010391.3654880956.27228654766.305442540368
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -a(n-4)
k=3: [order 18]
k=4: [order 72]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
n=3: [order 15] for n>17
n=4: [order 68] for n>69
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..0. .0..0..1..1. .0..1..1..1. .0..0..1..1
..1..1..0..0. .1..0..1..1. .1..1..0..0. .1..0..0..0. .1..0..0..1
..1..0..1..0. .0..1..0..1. .1..0..1..0. .1..1..1..1. .1..1..1..1
..0..0..1..1. .1..1..1..0. .1..0..0..1. .1..1..1..1. .0..0..1..1
..1..1..0..0. .0..0..0..1. .0..1..1..0. .1..0..0..1. .1..1..0..0
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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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