A279741 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 2, 0, 2, 6, 8, 0, 5, 14, 35, 26, 0, 8, 26, 106, 168, 80, 0, 15, 48, 286, 736, 766, 240, 0, 26, 84, 746, 2948, 4940, 3402, 708, 0, 46, 146, 1887, 11434, 29140, 32430, 14827, 2062, 0, 80, 250, 4700, 42494, 167904, 281350, 209558, 63680, 5944, 0, 139

Offset

1,4

Comments

Table starts

.0.....0.......2........2..........5...........8............15..............26

.0.....2.......6.......14.........26..........48............84.............146

.0.....8......35......106........286.........746..........1887............4700

.0....26.....168......736.......2948.......11434.........42494..........154886

.0....80.....766.....4940......29140......167904........927615.........5029822

.0...240....3402....32430.....281350.....2407152......19743140.......158848594

.0...708...14827...209558....2672708....33954530.....413326300......4935790522

.0..2062...63680..1337624...25057618...472691878....8539248826....151323545378

.0..5944..270313..8453760..232453138..6511502806..174560480712...4589874672896

.0.16990.1136546.52990574.2137856646.88926626284.3537506044402.137999764109606

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)

k=3: a(n) = 10*a(n-1) -35*a(n-2) +54*a(n-3) -45*a(n-4) +20*a(n-5) -4*a(n-6) for n>7

k=4: [order 16] for n>17

k=5: [order 25] for n>26

k=6: [order 64] for n>65

Empirical for row n:

n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5

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

n=3: [order 16] for n>18

n=4: [order 45] for n>50

Example

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

Crossrefs

Row 1 is A006367(n-1).

Sequence in context: A202015 A193350 A021458 * A099064 A280398 A052422

Adjacent sequences: A279738 A279739 A279740 * A279742 A279743 A279744

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 18 2016

Status

approved