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A280554
T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
7
0, 0, 0, 0, 0, 0, 1, 9, 9, 1, 2, 34, 50, 34, 2, 6, 87, 144, 144, 87, 6, 13, 194, 325, 382, 325, 194, 13, 29, 400, 670, 832, 832, 670, 400, 29, 60, 790, 1316, 1666, 1764, 1666, 1316, 790, 60, 122, 1511, 2502, 3182, 3438, 3438, 3182, 2502, 1511, 122, 241, 2830, 4654
OFFSET
1,8
COMMENTS
Table starts
...0....0....0.....1.....2.....6....13.....29.....60....122....241....468
...0....0....9....34....87...194...400....790...1511...2830...5213...9484
...0....9...50...144...325...670..1316...2502...4654...8521..15412..27612
...1...34..144...382...832..1666..3182...5886..10680..19122..33920..59754
...2...87..325...832..1764..3438..6386..11506..20389..35757..62317.108150
...6..194..670..1666..3438..6502.11697..20440..35226..60300.102974.175746
..13..400.1316..3182..6386.11697.20334..34360..57389..95548.159360.266756
..29..790.2502..5886.11506.20440.34360..56102..90614.146264.237392.388378
..60.1511.4654.10680.20389.35226.57389..90614.141398.220709.347310.553046
.122.2830.8521.19122.35757.60300.95548.146264.220709.332810.506359.781682
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)
k=2: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +10*a(n-4) -2*a(n-5) -5*a(n-6) +a(n-7) +a(n-8) for n>9
k=3: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +10*a(n-4) -2*a(n-5) -5*a(n-6) +a(n-7) +a(n-8) for n>10
k=4: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>11
k=5: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12
k=6: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12
k=7: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..1. .0..1..0..0. .0..1..1..0. .0..1..0..1. .0..1..0..1
..1..0..1..0. .0..1..0..1. .1..1..0..1. .0..1..0..1. .1..0..1..1
..0..1..1..0. .1..0..1..0. .0..0..1..0. .1..0..1..0. .0..1..0..0
..1..0..1..0. .0..0..1..0. .1..1..0..1. .1..1..0..0. .0..1..0..1
CROSSREFS
Column 1 is A055243(n-4).
Column 2 is A279128.
Sequence in context: A174266 A351722 A334425 * A195722 A133627 A268918
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 05 2017
STATUS
approved