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

1,1

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

Links

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

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

Example

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

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

Sequence in context: A081238 A333823 A207254 * A208142 A207024 A207169

Adjacent sequences: A207400 A207401 A207402 * A207404 A207405 A207406

Keyword

nonn,tabl

Author

R. H. Hardin Feb 17 2012

Status

approved