A188058 T(n,m)=Number of (n+1)X4 0..m arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors

42, 277, 51, 1098, 243, 111, 3265, 701, 942, 162, 7988, 1715, 4686, 1203, 270, 17119, 3343, 17015, 4810, 3190, 362, 33182, 5947, 49225, 15061, 20224, 4023, 590, 59629, 9789, 122034, 36032, 89650, 21760, 9982, 846, 100752, 15499, 269126, 75899, 306279

Offset

1,1

Comments

Table starts

...42...277...1098....3265.....7988....17119.....33182.....59629.....100752

...51...243....701....1715.....3343.....5947......9789.....15499......23561

..111...942...4686...17015....49225...122034....269126....542993....1017161

..162..1203...4810...15061....36032....75899....144828....261953.....447796

..270..3190..20224...89650...306279...877068...2196353...4964919...10305311

..362..4023..21760...85269...248504...617557...1359050...2770711....5270164

..590..9982..82632..453894..1851766..6170249..17630852..44790772..103237074

..846.13985.101108..494751..1737718..5056121..12757534..29281979...61864356

.1362.32390.344804.2328714.11287138.43638003.142040510.405174957.1036328059

.1998.48553.465884.2834305.11961916.40663383.117448824.303281985..711428874

Links

R. H. Hardin, Table of n, a(n) for n = 1..2035

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>(8+2*A072649(m)), except n>(7+2*A072649(m)) 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=4 m=4
..4..0..3..0....2..0..0..4....0..4..0..3....1..3..0..2....0..0..3..4
..0..4..0..3....2..0..0..0....0..0..4..0....0..0..3..0....0..0..0..3
..2..0..4..0....2..0..0..0....0..0..0..4....0..0..0..3....1..0..0..0
..0..2..0..4....0..2..0..0....2..0..0..0....1..0..0..0....0..1..0..0
..1..0..2..4....3..0..2..2....0..2..0..0....0..1..0..0....3..0..1..3

Crossrefs

Sequence in context: A234043 A323800 A309925 * A036463 A190534 A248466

Adjacent sequences: A188055 A188056 A188057 * A188059 A188060 A188061

Keyword

nonn,tabl

Author

R. H. Hardin Apr 21 2011

Status

approved