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A279709
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T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
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12
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1, 1, 2, 1, 2, 4, 2, 3, 5, 8, 3, 4, 11, 13, 16, 5, 6, 22, 42, 34, 32, 8, 9, 47, 125, 161, 89, 64, 13, 14, 102, 385, 717, 617, 233, 128, 21, 22, 224, 1195, 3245, 4121, 2364, 610, 256, 34, 35, 494, 3751, 14988, 27346, 23690, 9057, 1597, 512, 55, 56, 1089, 11823, 70220
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OFFSET
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1,3
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..221
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 5*a(n-1) -5*a(n-2) +2*a(n-3)
k=4: [order 8] for n>9
k=5: [order 12] for n>13
k=6: [order 32] for n>33
k=7: [order 60] for n>62
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) for n>3
n=2: a(n) = 2*a(n-1) -a(n-3)
n=3: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +4*a(n-4) -a(n-5) -a(n-7) -a(n-8)
n=4: [order 23] for n>25
n=5: [order 56] for n>64
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EXAMPLE
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Table starts
...1....1......1.......2.........3..........5............8............13
...2....2......3.......4.........6..........9...........14............22
...4....5.....11......22........47........102..........224...........494
...8...13.....42.....125.......385.......1195.........3751.........11823
..16...34....161.....717......3245......14988........70220........329692
..32...89....617....4121.....27346.....187484......1302321.......9047660
..64..233...2364...23690....230128....2342179.....24137862.....248664928
.128..610...9057..136181...1936687...29270275....447547408....6837220721
.256.1597..34699..782826..16300179..365809911...8297886949..187983779265
.512.4181.132938.4500021.137192011.4571688626.153848240903.5168463666199
Some solutions for n=4 k=4
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..0..1..0. .0..1..1..0. .0..1..0..0. .0..1..0..1. .0..1..1..0
..1..0..1..1. .0..0..1..1. .0..0..1..1. .0..1..0..1. .0..0..0..1
..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .1..1..0..1
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CROSSREFS
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Column 1 is A000079(n-1).
Column 2 is A001519.
Row 1 is A000045(n-1).
Row 2 is A001611.
Sequence in context: A206299 A276053 A117268 * A261880 A119538 A068309
Adjacent sequences: A279706 A279707 A279708 * A279710 A279711 A279712
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Dec 17 2016
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STATUS
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approved
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