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A298337
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 61, 113, 61, 3, 5, 216, 628, 628, 216, 5, 8, 793, 3641, 5663, 3641, 793, 8, 13, 2907, 21375, 51588, 51588, 21375, 2907, 13, 21, 10622, 124972, 479767, 755110, 479767, 124972, 10622, 21, 34, 38809, 730509, 4442111, 11244900
OFFSET
1,5
COMMENTS
Table starts
..0.....1.......1.........2...........3.............5...............8
..1.....4......17........61.........216...........793............2907
..1....17.....113.......628........3641.........21375..........124972
..2....61.....628......5663.......51588........479767.........4442111
..3...216....3641.....51588......755110......11244900.......166636876
..5...793...21375....479767....11244900.....268494008......6373591375
..8..2907..124972...4442111...166636876....6373591375....242019919082
.13.10622..730509..41117169..2469362361..151336485128...9195408207604
.21.38809.4271331.380674402.36605480121.3595159432175.349596064308984
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 13] for n>15
k=4: [order 48] for n>50
EXAMPLE
Some solutions for n=4 k=4
..0..0..0..0. .0..1..1..1. .0..0..1..1. .0..1..1..0. .0..0..0..1
..1..0..1..0. .1..0..0..1. .0..1..0..0. .0..0..1..0. .1..1..1..0
..1..0..1..0. .1..0..1..0. .0..1..0..0. .0..0..1..0. .1..1..0..1
..1..1..0..1. .1..0..0..0. .1..0..1..1. .0..1..1..0. .1..0..1..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A297917.
Sequence in context: A299607 A297923 A298547 * A299398 A299228 A300040
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 17 2018
STATUS
approved