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.

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

R. H. Hardin, Table of n, a(n) for n = 1..144

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

Adjacent sequences: A279899 A279900 A279901 * A279903 A279904 A279905

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 22 2016

Status

approved