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

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

R. H. Hardin, Table of n, a(n) for n = 1..1966

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

Adjacent sequences: A189171 A189172 A189173 * A189175 A189176 A189177

Keyword

nonn,tabl

Author

R. H. Hardin Apr 18 2011

Status

approved