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A298087
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.
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7
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0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 0, 2, 0, 0, 11, 3, 3, 11, 0, 0, 13, 1, 10, 1, 13, 0, 0, 34, 7, 28, 28, 7, 34, 0, 0, 65, 18, 76, 154, 76, 18, 65, 0, 0, 123, 52, 213, 520, 520, 213, 52, 123, 0, 0, 266, 144, 645, 1574, 2767, 1574, 645, 144, 266, 0, 0, 499, 405, 1852, 7204, 11202
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OFFSET
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1,8
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COMMENTS
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Table starts
.0...0...0....0.....0......0.......0........0.........0..........0...........0
.0...1...3....2....11.....13......34.......65.......123........266.........499
.0...3...0....3.....1......7......18.......52.......144........405........1124
.0...2...3...10....28.....76.....213......645......1852.......5642.......17016
.0..11...1...28...154....520....1574.....7204.....28790.....105055......437163
.0..13...7...76...520...2767...11202....66148....385999....2040394....11280309
.0..34..18..213..1574..11202...65218...479206...3481050...24695892...177272585
.0..65..52..645..7204..66148..479206..4883926..46039875..420410890..3947485108
.0.123.144.1852.28790.385999.3481050.46039875.603770100.7267200831.90210295443
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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) = a(n-1) +3*a(n-2) -4*a(n-4)
k=3: [order 16] for n>17
k=4: [order 57] for n>58
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EXAMPLE
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Some solutions for n=7 k=4
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0
..0..1..0..1. .0..1..0..1. .1..0..1..1. .0..1..0..1. .0..1..1..0
..1..1..0..1. .1..0..0..1. .1..1..1..1. .1..0..1..0. .1..0..1..0
..0..0..1..1. .0..1..0..1. .0..0..1..1. .1..0..1..0. .1..0..1..0
..0..0..0..0. .0..1..1..1. .0..1..0..0. .1..0..1..0. .1..0..1..0
..0..0..1..0. .1..0..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1
..0..0..1..1. .1..1..0..0. .0..0..1..1. .0..0..0..0. .0..0..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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