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