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A302427
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 11, 10, 16, 13, 25, 21, 21, 21, 32, 21, 65, 38, 42, 51, 42, 64, 34, 185, 88, 83, 148, 93, 86, 128, 55, 385, 188, 235, 372, 362, 207, 179, 256, 89, 649, 377, 532, 1359, 992, 879, 517, 370, 512, 144, 1489, 735, 1250, 4223, 4231, 2503, 2447
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...11...21....38.....88....188.....377......735......1557.......3288
...8..10...21...42....83....235....532....1250.....2839......6972......16274
..16..21...51..148...372...1359...4223...12765....36991....120577.....379049
..32..42...93..362...992...4231..14764...53851...182216....685166....2496115
..64..86..207..879..2503..12527..48037..204549...775916...3358602...13687791
.128.179..517.2447..7611..49454.227283.1171867..5110314..27366139..134037982
.256.370.1007.6306.21321.179252.940829.6104653.30957683.207165078.1213329113
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) +10*a(n-3) -8*a(n-4) for n>9
k=4: [order 42] for n>43
k=5: [order 21] for n>24
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: [order 18] for n>19
n=4: [order 68] for n>69
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..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. .1..1..0..1. .0..1..0..0. .1..1..0..1
..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
..1..0..0..1. .1..0..1..0. .0..1..0..1. .1..1..0..1. .0..1..0..0
..1..0..1..0. .1..0..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302164.
Sequence in context: A330265 A302163 A302635 * A303197 A059185 A302309
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 07 2018
STATUS
approved