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A299839
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
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7
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0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 142, 64, 3, 5, 236, 1000, 1000, 236, 5, 8, 888, 7388, 13850, 7388, 888, 8, 13, 3336, 54611, 198202, 198202, 54611, 3336, 13, 21, 12512, 402928, 2853873, 5544044, 2853873, 402928, 12512, 21, 34, 46928, 2973312
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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
..1.....4.......18.........64...........236..............888...............3336
..1....18......142.......1000..........7388............54611.............402928
..2....64.....1000......13850........198202..........2853873...........41026724
..3...236.....7388.....198202.......5544044........156175241.........4390323230
..5...888....54611....2853873.....156175241.......8606994457.......473261273932
..8..3336...402928...41026724....4390323230.....473261273932.....50892107038125
.13.12512..2973312..589665345..123389988671...26017342950926...5471622342472717
.21.46928.21942164.8475712818.3468206088400.1430440832008036.588340577558059509
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..199
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FORMULA
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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 9] for n>10
k=4: [order 22] for n>23
k=5: [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..0..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..1
..0..1..1..0. .0..0..1..0. .1..1..0..0. .0..1..1..0. .0..0..0..1
..0..1..0..1. .1..1..1..1. .0..0..0..1. .1..0..0..0. .0..0..0..1
..0..0..0..1. .0..0..0..0. .0..1..1..1. .0..1..0..0. .1..0..1..1
..1..1..1..1. .1..1..0..0. .1..0..0..1. .1..1..1..1. .1..0..1..1
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CROSSREFS
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Column 1 is A000045(n-1).
Column 2 is A231950(n-1).
Sequence in context: A299937 A299067 A299728 * A265178 A159766 A280284
Adjacent sequences: A299836 A299837 A299838 * A299840 A299841 A299842
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Feb 20 2018
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STATUS
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approved
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