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A299187
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 6 or 7 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 69, 27, 27, 69, 32, 64, 137, 47, 75, 47, 137, 64, 128, 301, 83, 191, 191, 83, 301, 128, 256, 705, 137, 401, 626, 401, 137, 705, 256, 512, 1461, 235, 952, 1442, 1442, 952, 235, 1461, 512, 1024, 3193, 412, 2258, 4115
OFFSET
1,2
COMMENTS
Table starts
...1....2...4....8....16.....32......64.....128......256.......512.......1024
...2....7..13...29....69....137.....301.....705.....1461......3193.......7373
...4...13..20...27....47.....83.....137.....235......412.......709.......1228
...8...29..27...75...191....401.....952....2258.....5275.....13250......32268
..16...69..47..191...626...1442....4115...12839....34387....101533.....306593
..32..137..83..401..1442...3773...12847...48408...157805....562522....2057541
..64..301.137..952..4115..12847...59287..270914..1088697...5017429...22861814
.128..705.235.2258.12839..48408..270914.1666826..8168186..46505377..277299195
.256.1461.412.5275.34387.157805.1088697.8168186.51863841.370258161.2763281188
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +8*a(n-3) -20*a(n-4) +8*a(n-5) for n>6
k=3: [order 17] for n>19
k=4: [order 67] for n>70
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..0. .0..0..1..0. .0..1..0..0. .0..0..1..1
..0..0..0..1. .1..0..0..1. .1..1..0..1. .0..1..1..1. .1..0..1..0
..0..0..1..0. .0..1..0..0. .0..0..0..1. .1..0..1..0. .1..1..1..0
..1..0..0..1. .1..0..0..0. .1..0..1..0. .1..0..1..0. .1..1..1..0
..1..1..0..1. .1..0..1..0. .1..0..1..0. .1..0..1..0. .1..0..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A297883.
Sequence in context: A298294 A299388 A298494 * A299948 A298221 A299350
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 04 2018
STATUS
approved