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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 2 is A016742

Row 1 is A171861(n+1)

Row 2 is A207025

Sequence in context: A208142 A207024 A207169 * A207305 A207391 A207938

Adjacent sequences: A207108 A207109 A207110 * A207112 A207113 A207114

Keyword

nonn,tabl

Author

R. H. Hardin Feb 15 2012

Status

approved