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A302680
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 3, 3, 4, 5, 3, 4, 8, 8, 5, 8, 6, 16, 13, 7, 12, 7, 9, 32, 21, 13, 18, 20, 11, 14, 64, 34, 23, 40, 30, 33, 18, 22, 128, 55, 37, 94, 76, 63, 64, 29, 35, 256, 89, 63, 184, 217, 187, 125, 121, 47, 56, 512, 144, 109, 358, 509, 661, 453, 257, 231, 76, 90, 1024, 233, 183, 760
OFFSET
1,2
COMMENTS
Table starts
...1..2..3...5....8...13....21.....34......55.......89......144.......233
...2..3..3...5....7...13....23.....37......63......109......183.......309
...4..4..8..12...18...40....94....184.....358......760.....1594......3220
...8..6..7..20...30...76...217....509....1189.....3034.....7569.....18274
..16..9.11..33...63..187...661...1837....5075....15661....46975....135191
..32.14.18..64..125..453..2013...6725...21745....80985...295335...1015113
..64.22.29.121..257.1125..6311..25139...96728...439233..1942666...8017639
.128.35.47.231..528.2782.19497..92889..422915..2330640.12480973..61679118
.256.56.76.440.1085.6843.60253.343421.1847358.12346637.80210343.474618407
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) -a(n-3)
k=3: a(n) = a(n-1) +a(n-2) for n>5
k=4: a(n) = a(n-1) +2*a(n-2) -a(n-4) for n>8
k=5: a(n) = a(n-1) +3*a(n-3) +2*a(n-4) +2*a(n-5) for n>10
k=6: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +a(n-4) -2*a(n-5) -a(n-6) for n>12
k=7: [order 12] for n>19
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +2*a(n-3) for n>5
n=3: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) for n>7
n=4: a(n) = a(n-1) +a(n-2) +5*a(n-3) +5*a(n-4) -3*a(n-5) -3*a(n-6) +2*a(n-7) for n>11
n=5: [order 11] for n>16
n=6: [order 17] for n>23
n=7: [order 31] for n>38
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..1. .0..1..0..1. .0..0..0..1. .0..1..1..1. .0..0..0..1
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..0..1..1. .0..1..1..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .1..1..0..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..0..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A001611(n+1).
Row 1 is A000045(n+1).
Row 2 is A003229(n-1) for n>2.
Sequence in context: A136537 A153928 A119446 * A302515 A303314 A349122
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 11 2018
STATUS
approved