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A218663
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T(n,k) = Hilltop maps: number of n X k binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..1 n X k array.
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14
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1, 3, 3, 5, 15, 5, 9, 57, 57, 9, 17, 225, 417, 225, 17, 31, 891, 3249, 3249, 891, 31, 57, 3519, 25533, 50625, 25533, 3519, 57, 105, 13905, 199489, 793881, 793881, 199489, 13905, 105, 193, 54945, 1560161, 12383361, 24879489, 12383361, 1560161, 54945
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OFFSET
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1,2
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COMMENTS
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From Andrew Howroyd, May 10 201: (Start)
Number of n X k binary matrices with every 1 adjacent to some 0 horizontally, vertically, diagonally or antidiagonally.
Number of dominating sets in the n X k king graph. (End)
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..240
Wikipedia, Dominating set
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) +a(n-3)
k=2: a(n) = 3*a(n-1) +3*a(n-2) +3*a(n-3)
k=3: a(n) = 6*a(n-1) +11*a(n-2) +26*a(n-3) -5*a(n-4) -5*a(n-6)
k=4: a(n) = 12*a(n-1) +45*a(n-2) +180*a(n-3) -27*a(n-4) -81*a(n-6)
Columns k=1..z+1 for an underlying 0..z array: a(n) = sum(i=1..2z+1){(2^k-1)*a(n-i)} checked for z=1..3.
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EXAMPLE
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Table starts
....1........3...........5...............9.................17
....3.......15..........57.............225................891
....5.......57.........417............3249..............25533
....9......225........3249...........50625.............793881
...17......891.......25533..........793881...........24879489
...31.....3519......199489........12383361..........775176415
...57....13905.....1560161.......193349025........24176619049
..105....54945....12202673......3018953025.......754066017977
..193...217107....95434773.....47135449449.....23517838102321
..355...857871...746388537....735942652641....733484062428443
..653..3389769..5837454753..11490533873361..22876204302519509
.1201.13394241.45654295713.179405691966081.713472099034206097
...
Some solutions for n=3 k=4
..1..1..1..0....1..0..1..1....0..1..0..1....0..1..1..0....1..0..0..0
..0..1..0..0....0..0..0..0....1..0..0..1....0..0..1..1....0..0..1..1
..0..1..0..1....1..1..0..1....0..1..1..1....1..1..0..1....1..1..0..0
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CROSSREFS
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Columns 1-7 are A000213(n+1), A218657, A218658, A218659, A218660, A218661, A218662.
Diagonal is A133791.
Cf. A218354, A221446, A219078, A218426.
Sequence in context: A133190 A052898 A183483 * A095355 A336130 A069834
Adjacent sequences: A218660 A218661 A218662 * A218664 A218665 A218666
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Nov 04 2012
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STATUS
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approved
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