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A300040
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
5
0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 61, 113, 61, 3, 5, 216, 628, 628, 216, 5, 8, 793, 3669, 5663, 3669, 793, 8, 13, 2907, 21792, 51862, 51862, 21792, 2907, 13, 21, 10622, 128610, 486305, 766231, 486305, 128610, 10622, 21, 34, 38809, 758715, 4532025, 11576060
OFFSET
1,5
COMMENTS
Table starts
..0.....1.......1.........2...........3.............5...............8
..1.....4......17........61.........216...........793............2907
..1....17.....113.......628........3669.........21792..........128610
..2....61.....628......5663.......51862........486305.........4532025
..3...216....3669.....51862......766231......11576060.......173419447
..5...793...21792....486305....11576060.....281861630......6789384478
..8..2907..128610...4532025...173419447....6789384478....262361247480
.13.10622..758715..42210111..2597671575..163627792463..10149632583491
.21.38809.4478515.393354513.38941599079.3947880819311.393165011518395
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 14] for n>16
k=4: [order 49] for n>51
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..0..0..1. .0..0..0..0
..1..0..1..0. .1..0..1..0. .1..0..1..1. .1..0..1..0. .0..1..0..1
..1..1..1..0. .0..1..0..0. .1..0..0..1. .1..0..1..0. .0..1..0..1
..0..0..0..1. .1..0..1..1. .1..1..1..0. .1..0..1..1. .0..1..0..1
..1..1..0..0. .0..0..1..1. .1..0..0..1. .0..1..0..1. .1..0..0..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A297917.
Column 3 is A299223.
Column 4 is A299224.
Sequence in context: A298337 A299398 A299228 * A206359 A297951 A298560
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 23 2018
STATUS
approved