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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 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)