A207305 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 0 vertically

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 13, 81, 98, 64, 10, 19, 169, 271, 200, 100, 12, 28, 361, 665, 643, 350, 144, 14, 41, 784, 1675, 1759, 1271, 556, 196, 16, 60, 1681, 4344, 4939, 3773, 2239, 826, 256, 18, 88, 3600, 11081, 14446, 11497, 7093, 3641, 1168, 324, 20, 129

Offset

1,1

Comments

Table starts

..2...4....6....9....13....19.....28......41......60.......88......129

..4..16...36...81...169...361....784....1681....3600.....7744....16641

..6..36...98..271...665..1675...4344...11081...28136....71908...183709

..8..64..200..643..1759..4939..14446...41505..118266...339548...975493

.10.100..350.1271..3773.11497..36868..116117..361408..1134028..3564401

.12.144..556.2239..7093.23091..79802..271023..906448..3057442.10340359

.14.196..826.3641.12169.41893.154228..558557.1985288..7118528.25615229

.16.256.1168.5581.19515.70537.274288.1050811.3937294.14887794.56536529

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) = (8/3)*n^4 + (49/3)*n^3 + (16/3)*n^2 - (43/3)*n + 3

k=6: a(n) = (4/15)*n^5 + (45/4)*n^4 + (199/6)*n^3 - (73/4)*n^2 - (373/30)*n + 5

k=7: a(n) = (187/60)*n^5 + (153/4)*n^4 + (455/12)*n^3 - (249/4)*n^2 + (209/30)*n + 4

Example

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

Crossrefs

Column 2 is A016742

Column 3 is A207106

Column 4 is A207107

Row 1 is A000930(n+3)

Row 2 is A207170

Sequence in context: A207024 A207169 A207111 * A207391 A207938 A207068

Adjacent sequences: A207302 A207303 A207304 * A207306 A207307 A207308

Keyword

nonn,tabl

Author

R. H. Hardin Feb 16 2012

Status

approved