A278280 T(n,k) = Number of n X k 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

0, 0, 0, 0, 2, 0, 0, 4, 5, 0, 0, 13, 25, 16, 0, 0, 36, 122, 136, 49, 0, 0, 109, 661, 1461, 839, 153, 0, 0, 317, 3723, 15728, 16842, 5013, 476, 0, 0, 938, 20736, 172091, 350649, 196726, 30370, 1483, 0, 0, 2754, 115446, 1870365, 7466627, 7974561, 2293193

Offset

1,5

Comments

Table starts

.0.....0.......0..........0.............0................0..................0

.0.....2.......4.........13............36..............109................317

.0.....5......25........122...........661.............3723..............20736

.0....16.....136.......1461.........15728...........172091............1870365

.0....49.....839......16842........350649..........7466627..........157609938

.0...153....5013.....196726.......7974561........329985827........13538466880

.0...476...30370....2293193.....180592726......14526103064......1158266740087

.0..1483..183403...26748095....4093629985.....640011857446.....99182079495633

.0..4619.1108525..311952675...92770708201...28192246592564...8491049196878995

.0.14388.6699034.3638315600.2102508396678.1241921389868057.726961954823301592

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

k=3: a(n) = 6*a(n-1) +3*a(n-2) -17*a(n-3) +19*a(n-5) -16*a(n-6) +8*a(n-7) for n>9.

k=4: [order 17] for n>19.

k=5: [order 44] for n>46.

k=6: [order 98] for n>101.

Empirical for row n:

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

n=3: [order 16].

n=4: [order 40].

Example

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

Crossrefs

Sequence in context: A117434 A131742 A257813 * A351403 A213370 A244138

Adjacent sequences: A278277 A278278 A278279 * A278281 A278282 A278283

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 16 2016

Status

approved