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A298547
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 61, 109, 61, 3, 5, 216, 588, 588, 216, 5, 8, 793, 3276, 4771, 3276, 793, 8, 13, 2907, 18500, 41762, 41762, 18500, 2907, 13, 21, 10622, 104034, 367315, 575754, 367315, 104034, 10622, 21, 34, 38809, 585134, 3215618, 7967553
OFFSET
1,5
COMMENTS
Table starts
..0.....1.......1.........2...........3.............5...............8
..1.....4......17........61.........216...........793............2907
..1....17.....109.......588........3276.........18500..........104034
..2....61.....588......4771.......41762........367315.........3215618
..3...216....3276.....41762......575754.......7967553.......109775311
..5...793...18500....367315.....7967553.....173576070......3761355239
..8..2907..104034...3215618...109775311....3761355239....128132389259
.13.10622..585134..28178880..1514903717...81677753297...4376310739604
.21.38809.3291766.246983338.20908710812.1774108927621.149522986489383
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4) for n>5
k=3: [order 12] for n>13
k=4: [order 36] for n>39
EXAMPLE
Some solutions for n=6 k=4
..0..0..1..0. .0..0..1..0. .0..0..1..0. .0..0..1..0. .0..0..1..0
..0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
..0..1..0..0. .0..1..0..0. .0..0..0..1. .0..1..0..0. .0..1..1..0
..1..1..0..1. .1..0..0..1. .1..1..0..1. .0..0..0..1. .0..0..0..0
..0..1..1..0. .0..1..1..0. .0..0..1..0. .1..1..1..0. .0..1..1..1
..1..0..0..1. .0..0..1..0. .1..1..0..0. .1..1..0..1. .0..0..0..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A297917.
Sequence in context: A298653 A299607 A297923 * A298337 A299398 A299228
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 21 2018
STATUS
approved