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A299595
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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1, 2, 2, 3, 1, 3, 5, 3, 3, 5, 8, 5, 5, 5, 8, 13, 8, 11, 11, 8, 13, 21, 15, 19, 23, 19, 15, 21, 34, 26, 35, 53, 53, 35, 26, 34, 55, 45, 65, 121, 113, 121, 65, 45, 55, 89, 80, 120, 250, 256, 256, 250, 120, 80, 89, 144, 140, 220, 533, 541, 576, 541, 533, 220, 140, 144, 233, 245
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OFFSET
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1,2
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COMMENTS
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Table starts
..1..2...3....5....8...13....21....34....55.....89....144....233.....377
..2..1...3....5....8...15....26....45....80....140....245....431.....756
..3..3...5...11...19...35....65...120...220....404....744...1369....2517
..5..5..11...23...53..121...250...533..1162...2490...5327..11465...24641
..8..8..19...53..113..256...541..1148..2488...5349..11453..24617...52916
.13.15..35..121..256..576..1225..2601..5625..12100..25921..55696..119716
.21.26..65..250..541.1225..2583..5488.11899..25570..54750.117697..252985
.34.45.120..533.1148.2601..5488.11656.25269..54309.116285.249968..537305
.55.80.220.1162.2488.5625.11899.25269.54738.117679.252010.541648.1164265
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LINKS
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FORMULA
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Empirical for diagonal: [linear recurrence of order 15] for n>18
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +2*a(n-3) +a(n-5) for n>6
k=3: a(n) = a(n-1) +2*a(n-3) +a(n-4) +a(n-5) for n>8
k=4..99: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..0
..1..0..0..1. .1..0..0..0. .1..0..0..0. .1..0..0..0. .0..0..0..1
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0
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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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