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A297923
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 4 king-move adjacent elements, with upper left element zero.
8
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, 18451, 41762, 41762, 18451, 2907, 13, 21, 10622, 103558, 366976, 575754, 366976, 103558, 10622, 21, 34, 38809, 581318, 3211086, 7960069
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.........18451..........103558
..2....61.....588......4771.......41762........366976.........3211086
..3...216....3276.....41762......575754.......7960069.......109611795
..5...793...18451....366976.....7960069.....173216147......3751364813
..8..2907..103558...3211086...109611795....3751364813....127727388127
.13.10622..581318..28124318..1511726778...81401727872...4359449485941
.21.38809.3263838.246367034.20851649928.1766726336073.148831641978201
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 9] for n>12
k=4: [order 31] for n>34
EXAMPLE
Some solutions for n=4 k=4
..0..1..1..1. .0..1..1..0. .0..0..0..0. .0..1..0..0. .0..0..1..0
..0..1..0..0. .0..1..0..1. .1..0..1..0. .0..0..1..0. .1..1..0..1
..1..0..1..0. .1..0..0..1. .1..0..1..0. .1..0..1..0. .0..1..0..1
..1..1..0..1. .0..1..1..1. .1..0..1..1. .1..0..0..0. .0..1..1..0
CROSSREFS
Column 1 is A000045(n-1).
Sequence in context: A298846 A298653 A299607 * A298547 A298337 A299398
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 08 2018
STATUS
approved