A208688 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 78, 81, 14, 26, 256, 282, 189, 196, 21, 42, 676, 768, 927, 490, 441, 31, 68, 1764, 2430, 2889, 3430, 1113, 961, 46, 110, 4624, 7086, 11727, 12096, 11067, 2449, 2116, 68, 178, 12100, 21588, 40581, 66094, 41013, 34627

Offset

1,1

Comments

Table starts

..2....4....6.....10.....16......26.......42........68........110.........178

..4...16...36....100....256.....676.....1764......4624......12100.......31684

..6...36...78....282....768....2430.....7086.....21588......64230......193554

..9...81..189....927...2889...11727....40581....154359.....554733.....2062215

.14..196..490...3430..12096...66094...269766...1331988....5795314....27403166

.21..441.1113..11067..41013..301035..1346961...8556723...42184905...249260739

.31..961.2449..34627.133207.1332721..6398617..53340739..290904031..2188890625

.46.2116.5474.111642.444912.6219706.31733422.358035204.2130519946.21086588370

Links

R. H. Hardin, Table of n, a(n) for n = 1..1360

Formula

Empirical for row n:

n=1: a(k)=a(k-1)+a(k-2)

n=2: a(k)=2*a(k-1)+2*a(k-2)-a(k-3)

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

n=4: a(k)=a(k-1)+10*a(k-2)+2*a(k-3)-10*a(k-4)

n=5: a(k)=a(k-1)+17*a(k-2)+4*a(k-3)-32*a(k-4)

n=6: a(k)=a(k-1)+26*a(k-2)+6*a(k-3)-78*a(k-4)

n=7: a(k)=a(k-1)+39*a(k-2)+9*a(k-3)-180*a(k-4)

Example

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

Crossrefs

Column 1 is A038718(n+2)

Column 2 is A207069

Column 3 is A207724

Row 1 is A006355(n+2)

Row 2 is A206981

Sequence in context: A207589 A208069 A208840 * A207774 A207661 A208555

Adjacent sequences: A208685 A208686 A208687 * A208689 A208690 A208691

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 01 2012

Status

approved