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A299398
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 6 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, 3641, 5663, 3641, 793, 8, 13, 2907, 21375, 51588, 51588, 21375, 2907, 13, 21, 10622, 124972, 479767, 755157, 479767, 124972, 10622, 21, 34, 38809, 730509, 4442111, 11246136
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......755157......11246136.......166665723
..5...793...21375....479767....11246136.....268557163......6375889022
..8..2907..124972...4442111...166665723....6375889022....242153450727
.13.10622..730509..41117169..2469920505..151409151272...9202140590865
.21.38809.4271331.380674402.36615834468.3597323154240.349916213368020
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=5 k=4
..0..1..1..1. .0..1..0..1. .0..1..0..0. .0..1..1..0. .0..1..1..1
..0..1..0..0. .0..0..1..0. .0..0..1..0. .0..0..0..1. .0..1..0..0
..0..1..1..0. .1..1..0..1. .0..0..0..1. .1..1..0..1. .0..1..1..0
..0..1..1..0. .0..1..0..1. .1..0..0..0. .1..0..1..0. .0..0..0..0
..1..0..0..1. .0..1..0..1. .0..1..0..0. .0..0..0..1. .1..1..1..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A297917.
Column 3 is A298332.
Column 4 is A298333.
Sequence in context: A297923 A298547 A298337 * A299228 A300040 A206359
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 09 2018
STATUS
approved