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A280069
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T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
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7
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1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 4, 3, 5, 9, 15, 15, 9, 5, 8, 19, 39, 52, 39, 19, 8, 13, 41, 104, 170, 170, 104, 41, 13, 21, 88, 281, 603, 790, 603, 281, 88, 21, 34, 189, 771, 2157, 3729, 3729, 2157, 771, 189, 34, 55, 406, 2122, 7777, 17468, 23564, 17468, 7777, 2122
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OFFSET
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1,7
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COMMENTS
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Table starts
..1...1....1......2.......3........5.........8..........13...........21
..1...1....2......4.......9.......19........41..........88..........189
..1...2....5.....15......39......104.......281.........771.........2122
..2...4...15.....52.....170......603......2157........7777........28195
..3...9...39....170.....790.....3729.....17468.......82769.......394904
..5..19..104....603....3729....23564....145485......915505......5786757
..8..41..281...2157...17468...145485...1188839.....9934415.....83159859
.13..88..771...7777...82769...915505...9934415...110266512...1225662273
.21.189.2122..28195..394904..5786757..83159859..1225662273..18113056960
.34.406.5858.102429.1890877.36671797.698377561.13669391105.268403179093
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..263
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) for n>3
k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) for n>4
k=3: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) +5*a(n-4) -2*a(n-5) -2*a(n-6) -a(n-7) for n>9
k=4: [order 15] for n>18
k=5: [order 35] for n>40
k=6: [order 87] for n>91
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..1..1..1. .0..1..1..0. .1..1..0..0. .0..0..0..0. .0..0..0..1
..0..0..0..1. .1..1..0..0. .1..1..1..0. .1..1..1..1. .1..1..1..1
..0..0..0..1. .1..1..0..0. .1..1..1..0. .1..1..1..1. .1..1..1..1
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CROSSREFS
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Column 1 is A000045(n-1).
Column 2 is A078039(n-2).
Sequence in context: A005862 A293254 A046052 * A202276 A029115 A029101
Adjacent sequences: A280066 A280067 A280068 * A280070 A280071 A280072
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Dec 25 2016
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STATUS
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approved
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