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

Author

R. H. Hardin Feb 16 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 2 is A016742

Column 3 is A207106

Column 4 is A207107

Row 1 is A000930(n+3)

Row 2 is A207170

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