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A268750
T(n,k)=Number of nXk binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.
8
2, 4, 4, 7, 11, 7, 13, 32, 32, 13, 23, 89, 143, 89, 23, 41, 244, 623, 623, 244, 41, 72, 659, 2615, 4110, 2615, 659, 72, 126, 1760, 10830, 26334, 26334, 10830, 1760, 126, 219, 4657, 44067, 165019, 255651, 165019, 44067, 4657, 219, 379, 12228, 177429, 1016807
OFFSET
1,1
COMMENTS
Table starts
...2.....4.......7........13..........23............41.............72
...4....11......32........89.........244...........659...........1760
...7....32.....143.......623........2615.........10830..........44067
..13....89.....623......4110.......26334........165019........1016807
..23...244....2615.....26334......255651.......2425799.......22577073
..41...659...10830....165019.....2425799......34732937......487682438
..72..1760...44067...1016807....22577073.....487682438....10319681062
.126..4657..177429...6183665...207252725....6746117783...215027310572
.219.12228..707163..37209717..1880654551...92215499119..4425392044505
.379.31899.2796840.221970102.16909709308.1248437108837.90177748184504
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) -a(n-4)
k=3: a(n) = 4*a(n-1) +8*a(n-2) -24*a(n-3) -38*a(n-4) +4*a(n-5) +12*a(n-6) -a(n-8)
k=4: [order 10]
k=5: [order 18]
k=6: [order 22]
k=7: [order 42]
EXAMPLE
Some solutions for n=4 k=4
..1..0..0..0. .0..0..0..0. .1..0..1..0. .0..1..0..0. .0..1..0..0
..0..1..0..1. .0..0..0..0. .0..1..0..0. .0..0..1..0. .1..0..1..0
..1..0..0..0. .1..0..0..0. .0..0..0..0. .0..1..0..0. .0..1..0..0
..0..0..0..1. .0..1..1..0. .0..1..0..1. .1..0..0..0. .1..0..0..0
CROSSREFS
Column 1 is A208354(n+1).
Sequence in context: A269089 A282862 A296578 * A282996 A295275 A295253
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 12 2016
STATUS
approved