A207111 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 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, 18, 169, 271, 200, 100, 12, 25, 324, 677, 643, 350, 144, 14, 34, 625, 1504, 1835, 1271, 556, 196, 16, 46, 1156, 3399, 4534, 4047, 2239, 826, 256, 18, 62, 2116, 7220, 11511, 10898, 7837, 3641, 1168, 324, 20, 83, 3844

Offset: 1

Author

R. H. Hardin Feb 15 2012

Keywords

• nonn
• tabl

Comments

Table starts

..2...4....6....9....13....18.....25.....34......46......62.......83......111

..4..16...36...81...169...324....625...1156....2116....3844.....6889....12321

..6..36...98..271...677..1504...3399...7220...15184...31664....64749...132543

..8..64..200..643..1835..4534..11511..27012...62814..144676...325111...733469

.10.100..350.1271..4047.10898..30415..77326..194952..486102..1177409..2870021

.12.144..556.2239..7837.22714..68737.187054..505040.1346150..3472283..9030485

.14.196..826.3641.13863.42874.139341.402498.1153962.3259098..8878431.24420005

.16.256.1168.5581.22931.75198.260597.794118.2402578.7142988.20426983.59031673

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..612

Crossrefs

Column 2 is A016742

Row 1 is A171861(n+1)

Row 2 is A207025

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) = (7/60)*n^5 + (8/3)*n^4 + (185/12)*n^3 + (19/3)*n^2 - (218/15)*n + 3

k=6: a(n) = (7/360)*n^6 + (77/120)*n^5 + (635/72)*n^4 + (623/24)*n^3 - (511/180)*n^2 - (103/5)*n + 6

k=7: a(n) = (1/280)*n^7 + (7/45)*n^6 + (47/15)*n^5 + (206/9)*n^4 + (4111/120)*n^3 - (1037/45)*n^2 - (4493/210)*n + 9