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A302163
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
13
1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 7, 10, 16, 13, 25, 12, 17, 21, 32, 21, 65, 20, 29, 31, 42, 64, 34, 185, 34, 51, 73, 57, 86, 128, 55, 385, 56, 109, 140, 156, 111, 179, 256, 89, 649, 94, 206, 296, 280, 361, 265, 370, 512, 144, 1489, 156, 407, 603, 635, 621, 865, 527, 770
OFFSET
1,2
COMMENTS
Table starts
...1...2...3....5....8...13....21....34....55.....89....144.....233.....377
...2...3...9...17...25...65...185...385...649...1489...3929....8609...15913
...4...6...7...12...20...34....56....94...156....262....436.....730....1216
...8..10..17...29...51..109...206...407...791...1584...3104....6165...12131
..16..21..31...73..140..296...603..1288..2584...5456..11189...23561...48423
..32..42..57..156..280..635..1247..2815..5524..12457..25230...55645..113410
..64..86.111..361..621.1563..2853..7306.12963..33522..61775..157788..293072
.128.179.265..865.1451.3948..6870.19993.32005.100147.163475..531350..820788
.256.370.527.1970.3189.9405.15489.50691.75825.282597.409385.1667452.2263018
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: a(n) = a(n-1) +8*a(n-3) -6*a(n-4) -4*a(n-6) +4*a(n-7) for n>11
k=4: [order 15] for n>19
k=5: [order 12] for n>15
k=6: [order 15] for n>26
k=7: [order 27] for n>39
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6
n=3: a(n) = a(n-1) +a(n-2) -a(n-3) +2*a(n-4) for n>6
n=4: [order 22] for n>23
n=5: [order 36] for n>40
n=6: [order 35] for n>45
n=7: [order 80] for n>89
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..0..1..1. .0..1..1..0
..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..1
..0..1..0..0. .0..1..0..1. .1..0..1..0. .0..1..1..0. .1..1..0..0
..0..1..0..1. .1..0..0..1. .1..0..1..0. .1..0..1..0. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Sequence in context: A374210 A036811 A330265 * A302635 A302427 A303197
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 02 2018
STATUS
approved