A207403 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 12, 81, 102, 64, 10, 16, 144, 289, 216, 100, 12, 20, 256, 612, 729, 390, 144, 14, 25, 400, 1296, 1782, 1521, 636, 196, 16, 30, 625, 2340, 4356, 4212, 2809, 966, 256, 18, 36, 900, 4225, 8910, 11664, 8692, 4761, 1392, 324, 20, 42, 1296

Offset: 1

Author

R. H. Hardin Feb 17 2012

Keywords

• nonn
• tabl

Comments

Table starts

..2...4....6....9....12.....16.....20.....25......30......36.......42.......49

..4..16...36...81...144....256....400....625.....900....1296.....1764.....2401

..6..36..102..289...612...1296...2340...4225....6890...11236....17066....25921

..8..64..216..729..1782...4356...8910..18225...33210...60516...101598...170569

.10.100..390.1521..4212..11664..26676..61009..123006..248004...456666...840889

.12.144..636.2809..8692..26896..68060.172225..380970..842724..1690038..3389281

.14.196..966.4761.16284..55696.154580.429025.1033590.2490084..5404650.11730625

.16.256.1392.7569.28362.106276.321110.970225.2529480.6594624.15405432.35988001

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1512

Crossrefs

Column 2 is A016742

Column 3 is A086113

Row 1 is A002620(n+2)

Row 2 is A030179(n+2)

Row 3 is A207118

Formula

Empirical for column k:

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

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

k=3: a(n) = 2*n^3 + 6*n^2 - 2*n

k=4: a(n) = n^4 + 6*n^3 + 7*n^2 - 6*n + 1

k=5: a(n) = (1/3)*n^5 + 3*n^4 + (28/3)*n^3 + 7*n^2 - (29/3)*n + 2

k=6: a(n) = (1/9)*n^6 + (4/3)*n^5 + (58/9)*n^4 + (40/3)*n^3 + (49/9)*n^2 - (44/3)*n + 4

k=7: a(n) = (1/36)*n^7 + (4/9)*n^6 + (53/18)*n^5 + (91/9)*n^4 + (589/36)*n^3 + (31/9)*n^2 - (58/3)*n + 6