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