A279657 T(n,k) = Number of n X k 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 0, 0, 3, 0, 3, 27, 24, 0, 6, 254, 734, 232, 0, 24, 2301, 19986, 20448, 2232, 0, 72, 19053, 498424, 1546164, 549608, 20880, 0, 232, 149696, 11256083, 104452983, 113887852, 14309072, 190656, 0, 720, 1124969, 239891281, 6415919752

Offset

1,5

Comments

Table starts

.0.......1..........0..............3..................6....................24

.0.......3.........27............254...............2301.................19053

.0......24........734..........19986.............498424..............11256083

.0.....232......20448........1546164..........104452983............6415919752

.0....2232.....549608......113887852........20868369045.........3484404510555

.0...20880...14309072.....8077041000......4019412007893......1824673552805793

.0..190656..362942080...556408163556....752482408442895....928920011450982106

.0.1707264.9010004672.37457887289336.137719420200247895.462385405050721564618

Links

R. H. Hardin, Table of n, a(n) for n = 1..110

Formula

Empirical for column k:

k=1: a(n) = a(n-1).

k=2: [order 6] for n>7.

k=3: [order 9] for n>10.

k=4: [order 24] for n>25.

k=5: [order 42] for n>43.

Empirical for row n:

n=1: a(n) = 6*a(n-1) -6*a(n-2) -16*a(n-3) +12*a(n-4) +24*a(n-5) +8*a(n-6) for n>8.

n=2: [order 13].

n=3: [order 51] for n>53.

Example

Some solutions for n=3, k=4
..0..0..0..1. .0..0..1..2. .0..0..0..1. .0..0..1..2. .0..1..0..2
..2..1..1..0. .0..1..2..2. .0..2..2..0. .0..1..2..0. .2..1..1..0
..1..0..1..2. .2..1..0..2. .0..0..2..1. .2..0..2..1. .1..2..0..0

Crossrefs

Row 1 is A279300.

Sequence in context: A128252 A230675 A327673 * A272722 A229694 A033596

Adjacent sequences: A279654 A279655 A279656 * A279658 A279659 A279660

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 16 2016

Status

approved