A207391 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 14, 81, 98, 64, 10, 21, 196, 271, 200, 100, 12, 31, 441, 834, 643, 350, 144, 14, 46, 961, 2307, 2356, 1271, 556, 196, 16, 68, 2116, 6115, 7561, 5348, 2239, 826, 256, 18, 100, 4624, 16544, 23071, 19319, 10570, 3641, 1168, 324, 20, 147

Offset

1,1

Comments

Table starts

..2...4....6....9....14.....21.....31......46.......68......100.......147

..4..16...36...81...196....441....961....2116.....4624....10000.....21609

..6..36...98..271...834...2307...6115...16544....44250...116526....307117

..8..64..200..643..2356...7561..23071...72410...223804...678174...2060069

.10.100..350.1271..5348..19319..65955..232892...806886..2731598...9282799

.12.144..556.2239.10570..42167.158217..616386..2348280..8718366..32527713

.14.196..826.3641.18972..82477.335915.1424240..5887228.23664574..95673277

.16.256.1168.5581.31710.148743.651531.2975974.13215696.56972122.247183399

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

Formula

Empirical for column k:

k=1: a(n) = 2*n

k=2: a(n) = 4*n^2

k=3: a(n) = (4/3)*n^3 + 8*n^2 - (10/3)*n

k=4: a(n) = (5/12)*n^4 + (13/2)*n^3 + (115/12)*n^2 - (17/2)*n + 1

k=5: a(n) = (2/15)*n^5 + (55/12)*n^4 + (101/6)*n^3 + (5/12)*n^2 - (299/30)*n + 2

k=6: a(n) = (1/36)*n^6 + (113/60)*n^5 + (151/9)*n^4 + (95/4)*n^3 - (605/36)*n^2 - (229/30)*n + 3

k=7: a(n) = (1/210)*n^7 + (103/180)*n^6 + (197/20)*n^5 + (1439/36)*n^4 + (293/20)*n^3 - (3469/90)*n^2 + (157/105)*n + 3

Example

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

Crossrefs

Column 1 is A004275(n+1)

Column 2 is A016742

Column 3 is A207106

Column 4 is A207107

Row 1 is A038718(n+2)

Row 2 is A207069

Sequence in context: A207169 A207111 A207305 * A207938 A207068 A209650

Adjacent sequences: A207388 A207389 A207390 * A207392 A207393 A207394

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 17 2012

Status

approved