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A190023 T(n,m)=Number of (n+1)X3 0..m arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors 1
21, 83, 30, 205, 129, 51, 419, 362, 243, 88, 713, 839, 701, 562, 128, 1169, 1638, 1715, 2049, 903, 197, 1709, 2923, 3343, 5879, 3442, 1754, 292, 2471, 4834, 5947, 13342, 10259, 8223, 2937, 457, 3381, 7605, 9789, 26982, 23790, 28628, 14492, 5790, 688 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...21....83....205....419.....713....1169.....1709.....2471......3381......4543

...30...129....362....839....1638....2923.....4834.....7605.....11434.....16493

...51...243....701...1715....3343....5947.....9789....15499.....23561.....33877

...88...562...2049...5879...13342...26982....49867....87001....143918....224458

..128...903...3442..10259...23790...48875....91096...160377....267770....420837

..197..1754...8223..28628...77358..181792...383152...749237...1371936...2357920

..292..2937..14492..53045..146406..349085...740408..1460393...2698956...4662219

..457..5790..35081.150208..481171.1308972..3134584..6868867..13933702..26279979

..688..9993..64280.289063..945714.2606517..6273818.13842067..28288458..53533915

.1058.19236.150785.792360.3006488.9456818.25715484.63104546.141749332.293291390

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..2450

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>(7+2*A072649(m)), except for n>8 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

..3..0..0....0..4..0....3..3..3....3..3..0....0..1..3....2..3..0....4..2..0

..3..0..0....3..0..4....0..0..0....0..0..3....0..0..1....0..0..3....3..0..2

..0..3..0....0..3..0....0..0..0....0..0..0....0..0..0....0..0..0....0..3..0

..2..0..3....1..0..3....3..0..0....0..0..0....1..0..0....2..0..0....3..0..3

..0..2..4....0..1..0....4..3..0....2..2..2....4..1..0....0..2..1....0..3..1

CROSSREFS

Sequence in context: A159743 A219593 A195961 * A071397 A064762 A104676

Adjacent sequences:  A190020 A190021 A190022 * A190024 A190025 A190026

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin May 04 2011

STATUS

approved

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Last modified October 21 07:01 EDT 2019. Contains 328292 sequences. (Running on oeis4.)