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A299373
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 130, 64, 3, 5, 236, 876, 876, 236, 5, 8, 888, 6025, 10692, 6025, 888, 8, 13, 3336, 41528, 136106, 136106, 41528, 3336, 13, 21, 12512, 285931, 1736688, 3216110, 1736688, 285931, 12512, 21, 34, 46928, 1968966
OFFSET
1,5
COMMENTS
Table starts
..0.....1........1..........2.............3...............5.................8
..1.....4.......18.........64...........236.............888..............3336
..1....18......130........876..........6025...........41528............285931
..2....64......876......10692........136106.........1736688..........22129704
..3...236.....6025.....136106.......3216110........76033854........1795186406
..5...888....41528....1736688......76033854......3330673422......145700454710
..8..3336...285931...22129704....1795186406....145700454710....11808073517522
.13.12512..1968966..281996650...42387096961...6374113851083...957054636207245
.21.46928.13558267.3593547434.1000847932823.278862313827105.77572170112847769
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3) for n>4
k=3: [order 10] for n>11
k=4: [order 31] for n>32
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..1..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..0
..0..0..0..1. .0..1..1..1. .0..0..0..0. .1..1..1..0. .0..0..0..0
..0..0..0..1. .1..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0
..1..1..1..0. .1..0..0..0. .1..1..1..1. .0..0..0..1. .1..1..1..1
..0..0..0..1. .1..0..0..0. .1..1..0..0. .0..0..0..1. .1..0..0..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A231950(n-1).
Sequence in context: A300108 A298280 A299142 * A299937 A299067 A299728
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 08 2018
STATUS
approved