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A299388
T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 4, 6 or 8 king-move adjacent elements, with upper left element zero.
5
1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 69, 26, 26, 69, 32, 64, 137, 43, 46, 43, 137, 64, 128, 301, 72, 130, 130, 72, 301, 128, 256, 705, 115, 233, 310, 233, 115, 705, 256, 512, 1461, 189, 448, 531, 531, 448, 189, 1461, 512, 1024, 3193, 318, 877, 1112
OFFSET
1,2
COMMENTS
Table starts
...1....2...4....8...16...32....64...128....256....512....1024....2048....4096
...2....7..13...29...69..137...301...705...1461...3193....7373...15729...34405
...4...13..20...26...43...72...115...189....318....526.....874....1473....2482
...8...29..26...46..130..233...448...877...1605...3284....6774...13516...26780
..16...69..43..130..310..531..1112..2418...4870..10382...21883...45941...97484
..32..137..72..233..531.1002..1852..4200...9436..19203...41599...91092..197402
..64..301.115..448.1112.1852..4929.11412..24191..59037..137098..312216..728670
.128..705.189..877.2418.4200.11412.28917..66656.169277..416130..999147.2499437
.256.1461.318.1605.4870.9436.24191.66656.170693.444484.1173512.3002664.7845019
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=7, k=7
..0..0..0..1..1..0..0. .0..0..0..1..1..0..0. .0..1..1..1..1..0..1
..1..1..1..1..1..1..1. .1..1..1..0..0..1..1. .1..1..1..0..1..0..1
..0..1..1..1..0..1..0. .0..0..0..0..1..0..1. .0..0..0..0..1..1..0
..0..1..1..1..0..0..1. .1..0..0..0..0..1..1. .1..0..0..0..1..1..1
..1..1..1..1..1..1..0. .1..0..0..0..1..1..1. .1..0..0..0..0..1..1
..1..1..0..0..0..1..1. .0..0..0..0..1..1..0. .1..0..1..1..1..1..0
..1..0..1..1..1..0..0. .1..1..1..0..1..0..1. .0..1..0..0..0..1..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A297883.
Column 3 is A298289.
Column 4 is A298290.
Sequence in context: A270246 A297889 A298294 * A298494 A299187 A299948
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 09 2018
STATUS
approved