A188837 T(n,m)=Number of (n+1)X6 0..m arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors

106, 966, 128, 4895, 903, 270, 17608, 3442, 3190, 449, 50755, 10259, 20224, 4875, 797, 125368, 23790, 89650, 25633, 13278, 1061, 275175, 48875, 306279, 100789, 107353, 16083, 1681, 553211, 91096, 877068, 285899, 575344, 108025, 40626, 2285, 1033069

Offset

1,1

Comments

Table starts

..106....966....4895....17608....50755....125368.....275175.....553211

..128....903....3442....10259....23790.....48875......91096.....160377

..270...3190...20224....89650...306279....877068....2196353....4964919

..449...4875...25633...100789...285899....696553....1510299....3080551

..797..13278..107353...575344..2297416...7513081...21122896...52962480

.1061..16083..108025...510469..1702449...4754437...11602073...26225513

.1681..40626..433513..2895594.13845490..52753837..169362234..477196301

.2285..52755..479785..2857149.11562609..38012473..106808569..272285867

.3681.129102.1793817.14788974.84196426.372605789.1363387642.4314623879

.5281.182841.2226665.16533319.80688693.310706825.1001273881.2871421085

Links

R. H. Hardin, Table of n, a(n) for n = 1..1718

Formula

Empirical for column m: a(n) = 2*a(n-1) +(m-1)*a(n-2) -2*m*a(n-3) +2*m*a(n-4) -m*a(n-5) for n>(10+2*A072649(m)), except n>11 for m=1

Empirical more generally for column m of T(n,m,k) for (n+1)X(k+1) 0..m arrays: a(n) = 2*a(n-1) +(m-1)*a(n-2) -2*m*a(n-3) +2*m*a(n-4) -m*a(n-5) for n>(k+5+2*A072649(m)), except n>(k+4+2*A072649(m)) for m=1 and k>1

Example

Some solutions for n=3 m=3
..1..1..0..3..0..0....3..0..0..1..0..2....2..2..0..2..0..3....2..0..0..2..0..2
..1..0..1..0..3..0....3..0..0..0..1..0....0..0..2..0..2..0....2..0..0..0..2..0
..0..1..0..1..0..3....0..3..0..0..0..1....0..0..0..2..0..2....0..2..0..0..0..2
..1..0..1..0..1..3....2..0..3..0..0..2....1..0..0..0..2..0....2..0..2..0..0..1

Crossrefs

Sequence in context: A090037 A187588 A051974 * A184217 A184209 A373133

Adjacent sequences: A188834 A188835 A188836 * A188838 A188839 A188840

Keyword

nonn,tabl

Author

R. H. Hardin Apr 12 2011

Status

approved