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A301541
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 3 horizontally or vertically adjacent elements, with upper left element zero.
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7
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1, 2, 2, 3, 3, 3, 5, 6, 6, 5, 8, 10, 9, 10, 8, 13, 21, 26, 26, 21, 13, 21, 42, 61, 79, 61, 42, 21, 34, 86, 154, 212, 212, 154, 86, 34, 55, 179, 374, 603, 658, 603, 374, 179, 55, 89, 370, 941, 1841, 2417, 2417, 1841, 941, 370, 89, 144, 770, 2357, 5663, 9037, 10783, 9037
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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
..2...3....6....10.....21.....42......86......179.......370........770
..3...6....9....26.....61....154.....374......941......2357.......5963
..5..10...26....79....212....603....1841.....5663.....17379......53565
..8..21...61...212....658...2417....9037....33526....125626.....477972
.13..42..154...603...2417..10783...47791...215362....990403....4616134
.21..86..374..1841...9037..47791..255406..1432328...8145489...46701775
.34.179..941..5663..33526.215362.1432328..9891331..68863154..484837793
.55.370.2357.17379.125626.990403.8145489.68863154.588765472.5132456266
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..241
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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) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 20]
k=4: [order 62]
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..1..0..1..0. .1..1..1..0. .1..0..1..0. .1..1..1..0. .0..0..1..1
..1..1..0..0. .0..0..0..1. .0..1..0..0. .0..0..0..0. .0..1..0..1
..1..0..1..0. .1..0..1..0. .1..0..1..0. .1..0..0..0. .1..0..1..0
..0..1..0..1. .0..1..1..1. .0..1..1..1. .1..0..1..0. .1..0..1..0
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CROSSREFS
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Column 1 is A000045(n+1).
Column 2 is A240513.
Sequence in context: A049747 A260684 A029093 * A240519 A318037 A326165
Adjacent sequences: A301538 A301539 A301540 * A301542 A301543 A301544
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Mar 23 2018
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STATUS
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approved
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