A186484 T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors

625, 419, 419, 3265, 839, 3265, 3335, 1715, 1715, 3335, 17608, 5879, 17015, 5879, 17608, 19617, 10259, 15061, 15061, 10259, 19617, 89163, 28628, 89650, 64680, 89650, 28628, 89163, 110707, 53045, 85269, 100789, 100789, 85269, 53045, 110707, 459455

Offset

1,1

Comments

Table starts

....625....419....3265....3335....17608....19617....89163....110707....459455

....419....839....1715....5879....10259....28628....53045....150208....289063

...3265...1715...17015...15061....89650....85269...453894....494751...2328714

...3335...5879...15061...64680...100789...319970...489029...1667870...2708279

..17608..10259...89650..100789...575344...510469..2895594...2857149..14788974

..19617..28628...85269..319970...510469..1759744..2398869...9184194..12853549

..89163..53045..453894..489029..2895594..2398869.15145144..13490069..77860794

.110707.150208..494751.1667870..2857149..9184194.13490069..52024944..69802869

.459455.289063.2328714.2708279.14788974.12853549.77860794..69802869.422063944

.624228.792360.2834305.8719842.16533319.47290374.77119949.270513394.391681269

Links

R. H. Hardin, Table of n, a(n) for n = 1..647

Formula

Empirical, for every column: a(n)=2*a(n-1)+3*a(n-2)-8*a(n-3)+8*a(n-4)-4*a(n-5) for n>k+11

Example

Some solutions for 4X3
..0..0..4....1..1..0....4..4..0....4..2..0....4..4..0....1..4..0....1..4..0
..0..0..0....3..0..1....0..0..4....0..0..2....2..0..4....1..0..4....0..0..4
..3..0..0....0..3..0....0..0..2....0..0..0....0..2..0....0..1..0....0..0..0
..0..3..4....3..0..3....0..0..1....3..0..0....2..0..2....0..0..1....4..0..0

Crossrefs

Sequence in context: A115484 A005081 A210115 * A184037 A186483 A043352

Adjacent sequences: A186481 A186482 A186483 * A186485 A186486 A186487

Keyword

nonn,tabl

Author

R. H. Hardin Feb 22 2011

Status

approved