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A218663 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. 12
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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)

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..240

Wikipedia, Dominating set

FORMULA

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.

EXAMPLE

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

CROSSREFS

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 A069834 A064038

Adjacent sequences:  A218660 A218661 A218662 * A218664 A218665 A218666

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 04 2012

STATUS

approved

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Last modified October 22 09:56 EDT 2019. Contains 328315 sequences. (Running on oeis4.)