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A302635
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 8, 10, 16, 13, 25, 14, 19, 21, 32, 21, 65, 25, 33, 42, 42, 64, 34, 185, 47, 65, 101, 82, 86, 128, 55, 385, 83, 149, 257, 248, 189, 179, 256, 89, 649, 150, 304, 691, 719, 657, 469, 370, 512, 144, 1489, 269, 643, 1734, 2262, 2303, 1841, 1029
OFFSET
1,2
COMMENTS
Table starts
...1...2....3....5.....8.....13.....21......34.......55.......89.......144
...2...3....9...17....25.....65....185.....385......649.....1489......3929
...4...6....8...14....25.....47.....83.....150......269......488.......876
...8..10...19...33....65....149....304.....643.....1343.....2880......6038
..16..21...42..101...257....691...1734....4502....11524....30121.....77399
..32..42...82..248...719...2262...6460...19799....59002...179668....535412
..64..86..189..657..2303...8981..30216..112431...408512..1512824...5441957
.128.179..469.1841..7695..35772.144266..652931..2863575.12800635..55765517
.256.370.1029.4892.24205.135125.642553.3499587.18446157.98898783.515558643
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) +9*a(n-3) -4*a(n-4) +2*a(n-5) -10*a(n-6) +4*a(n-7) +4*a(n-9) for n>13
k=4: [order 21] for n>25
k=5: [order 29] for n>32
k=6: [order 54] for n>65
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) +2*a(n-4) -a(n-5) for n>7
n=4: [order 22] for n>23
n=5: [order 63] for n>64
n=6: [order 81] for n>86
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..0..1..1. .0..1..0..1
..1..1..1..0. .0..1..0..1. .0..1..0..0. .0..1..0..1. .0..0..0..1
..0..0..0..0. .0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..1..1. .0..1..0..1. .0..0..1..0. .0..1..0..1. .0..1..0..1
..0..1..0..0. .0..1..0..1. .1..1..1..0. .0..0..1..1. .0..1..1..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302164.
Sequence in context: A036811 A330265 A302163 * A302427 A303197 A059185
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 10 2018
STATUS
approved