A280180 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 1, 0, 2, 0, 3, 12, 12, 3, 3, 41, 60, 41, 3, 9, 103, 279, 279, 103, 9, 15, 263, 1082, 1633, 1082, 263, 15, 31, 656, 3931, 8759, 8759, 3931, 656, 31, 57, 1618, 13720, 43094, 63336, 43094, 13720, 1618, 57, 108, 3931, 46467, 202693, 421214, 421214, 202693, 46467

Offset: 1

Author

R. H. Hardin, Dec 28 2016

Keywords

• nonn
• tabl

Comments

Table starts

...0....1......0........3.........3...........9...........15.............31

...1....2.....12.......41.......103.........263..........656...........1618

...0...12.....60......279......1082........3931........13720..........46467

...3...41....279.....1633......8759.......43094.......202693.........919058

...3..103...1082.....8759.....63336......421214......2665301.......16203600

...9..263...3931....43094....421214.....3755997.....31821879......258976696

..15..656..13720...202693...2665301....31821879....359880117.....3910652938

..31.1618..46467...919058..16203600...258976696...3910652938....56789421603

..57.3931.153650..4057457..95738359..2046791216..41205820599...798794739075

.108.9459.499289.17554353.553426602.15814457993.424186764568.10974204206787

Examples

			Some solutions for n=4 k=4
..0..0..1..0. .0..0..0..0. .0..0..0..1. .0..1..1..1. .0..1..1..1
..0..1..0..0. .0..1..0..0. .0..0..0..0. .0..1..1..1. .1..1..1..1
..1..1..0..1. .0..0..0..0. .1..1..1..1. .0..1..0..0. .1..1..1..0
..1..1..0..0. .1..1..1..1. .1..1..1..1. .1..0..0..0. .1..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

Crossrefs

Column 1 is A105423(n-2).

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)

k=2: [order 10] for n>14

k=3: [order 21] for n>28

k=4: [order 45] for n>54