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A279902
T(n,k)=Number of nXk 0..2 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
7
0, 0, 0, 2, 4, 2, 2, 6, 6, 2, 8, 8, 9, 8, 8, 14, 18, 20, 20, 18, 14, 36, 36, 43, 56, 43, 36, 36, 74, 78, 94, 156, 156, 94, 78, 74, 168, 160, 213, 428, 601, 428, 213, 160, 168, 358, 338, 456, 1208, 2006, 2006, 1208, 456, 338, 358, 780, 700, 1003, 3316, 7383, 8384, 7383, 3316
OFFSET
1,4
COMMENTS
Table starts
...0...0....2.....2......8......14.......36.......74......168.......358
...0...4....6.....8.....18......36.......78......160......338.......700
...2...6....9....20.....43......94......213......456.....1003......2146
...2...8...20....56....156.....428.....1208.....3316.....9168.....25200
...8..18...43...156....601....2006.....7383....25400....89693....315334
..14..36...94...428...2006....8384....38532...165560...732174...3256516
..36..78..213..1208...7383...38532...226675..1231402..6889841..38738950
..74.160..456..3316..25400..165560..1231402..8386164.58985354.419342264
.168.338.1003..9168..89693..732174..6889841.58985354
.358.700.2146.25200.315334.3256516.38738950
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4) for n>5
k=2: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4) for n>7
k=3: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4) for n>7
k=4: [order 20] for n>23
k=5: [order 24] for n>27
EXAMPLE
Some solutions for n=4 k=4
..0..0..1..1. .0..0..0..0. .0..0..0..0. .0..1..1..1. .0..0..0..0
..0..0..1..1. .0..0..0..0. .1..0..0..0. .0..0..1..1. .0..0..0..0
..0..0..1..1. .1..1..1..0. .2..2..2..2. .0..0..1..1. .0..0..1..1
..0..2..1..1. .1..1..1..1. .2..2..2..2. .0..0..1..1. .0..1..1..1
CROSSREFS
Column 1 is 2*A219754(n+1).
Sequence in context: A055097 A258751 A280233 * A331004 A278540 A280161
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 22 2016
STATUS
approved