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

1,5

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

Links

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

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

Example

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

Crossrefs

Column 1 is A105423(n-2).

Sequence in context: A368584 A368583 A365547 * A337995 A337994 A135433

Adjacent sequences: A280177 A280178 A280179 * A280181 A280182 A280183

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 28 2016

Status

approved