A278094 T(n,k)=Number of nXk 0..1 arrays with every element both equal and not equal to some elements at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

0, 0, 0, 0, 2, 0, 0, 3, 3, 0, 0, 10, 16, 10, 0, 0, 27, 66, 66, 27, 0, 0, 76, 351, 670, 351, 76, 0, 0, 214, 1758, 6285, 6285, 1758, 214, 0, 0, 599, 9033, 61123, 114028, 61123, 9033, 599, 0, 0, 1683, 46159, 588464, 2066549, 2066549, 588464, 46159, 1683, 0, 0, 4721, 236245

Offset

1,5

Comments

Table starts

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

.0....2.......3........10...........27.............76...............214

.0....3......16........66..........351...........1758..............9033

.0...10......66.......670.........6285..........61123............588464

.0...27.....351......6285.......114028........2066549..........37564017

.0...76....1758.....61123......2066549.......70793904........2422349439

.0..214....9033....588464.....37564017.....2422349439......156188151088

.0..599...46159...5678912....682015651....82874815951....10066675051315

.0.1683..236245..54772100..12386272982..2835664463158...648924377800150

.0.4721.1208622.528291059.224933023893.97019475542749.41828515552220496

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

k=3: [order 13] for n>16

k=4: [order 33] for n>35

k=5: [order 86] for n>90

Example

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

Crossrefs

Sequence in context: A334218 A342984 A342985 * A245487 A074734 A174956

Adjacent sequences: A278091 A278092 A278093 * A278095 A278096 A278097

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 11 2016

Status

approved