editing

approved

R. H. Hardin, <a href="/A279856/b279856.txt">Table of n, a(n) for n = 1..112</a>

allocated for R. H. Hardin

T(n,k)=Number of nXk 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical 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, 10, 10, 2, 8, 24, 49, 24, 8, 14, 54, 168, 168, 54, 14, 36, 116, 557, 972, 557, 116, 36, 74, 250, 1758, 5200, 5200, 1758, 250, 74, 168, 528, 5441, 26632, 44893, 26632, 5441, 528, 168, 358, 1118, 16500, 134898, 373516, 373516, 134898, 16500

1,4

Table starts

...0....0......2........2..........8..........14..........36..........74

...0....4.....10.......24.........54.........116.........250.........528

...2...10.....49......168........557........1758........5441.......16500

...2...24....168......972.......5200.......26632......134898......668668

...8...54....557.....5200......44893......373516.....3010179....23836450

..14..116...1758....26632.....373516.....4989784....64921744...827573664

..36..250...5441...134898....3010179....64921744..1356293555.27796618392

..74..528..16500...668668...23836450...827573664.27796618392

.168.1118..49253..3278294..185854745.10392951988

.358.2348.145290.15902088.1432781380

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) = 3*a(n-1) +a(n-2) -7*a(n-3) +4*a(n-5)

k=3: a(n) = 4*a(n-1) -2*a(n-2) -9*a(n-4) -4*a(n-5) -4*a(n-6) for n>9

k=4: [order 38] for n>41

Some solutions for n=4 k=4

..0..1..1..1. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1

..0..1..1..1. .0..0..1..1. .0..0..0..1. .1..1..0..1. .0..0..0..1

..2..2..1..1. .0..2..2..1. .2..0..0..1. .1..1..0..0. .0..0..0..1

..2..2..2..2. .0..2..2..1. .0..0..0..1. .0..0..0..0. .0..0..1..1

Column 1 is A219754(n+1)*2.

allocated

nonn,tabl

R. H. Hardin, Dec 20 2016

approved

editing

allocated for R. H. Hardin

allocated

approved