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A189174
T(n,m)=Number of (n+1)X5 0..m arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors
1
61, 367, 88, 1251, 562, 162, 3335, 2049, 1203, 309, 7147, 5879, 4810, 3186, 449, 13411, 13342, 15061, 16762, 4875, 673, 23215, 26982, 36032, 64680, 25633, 9834, 945, 38239, 49867, 75899, 187120, 100789, 67714, 14883, 1493, 59909, 87001, 144828, 464292
OFFSET
1,1
COMMENTS
Table starts
...61....367....1251....3335.....7147.....13411.....23215......38239......59909
...88....562....2049....5879....13342.....26982.....49867......87001.....143918
..162...1203....4810...15061....36032.....75899....144828.....261953.....447796
..309...3186...16762...64680...187120....464292...1024481....2088749....3962712
..449...4875...25633..100789...285899....696553...1510299....3080551....5881273
..673...9834...67714..319970..1112735...3225157...8146732...18630316...39083491
..945..14883..101305..489029..1638899...4596421..11226859...25435323...53590349
.1493..31866..286290.1667870..6889391..23135705..66448348..170531687..396389352
.2201..51057..456113.2708279.10790363..35032589..97175595..246073869..572364869
.3473.105398.1219034.8719842.42654663.165747519.541063232.1556757087.4010340216
LINKS
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>(9+2*A072649(m)), except n>10 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..0..0..0..2....1..0..0..2..3....0..0..3..0..2....1..0..2..0..1
..3..0..0..0..0....0..0..0..0..2....0..0..0..3..0....0..1..0..2..0
..0..3..0..0..0....0..0..0..0..0....3..0..0..0..3....1..0..1..0..2
..1..0..3..0..0....1..0..0..0..0....0..3..0..0..3....0..1..0..1..1
CROSSREFS
Sequence in context: A357965 A353225 A373520 * A304062 A305454 A266134
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Apr 18 2011
STATUS
approved