A206215 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..2 introduced in row major order

14, 45, 45, 162, 130, 162, 594, 336, 336, 594, 2268, 992, 760, 992, 2268, 8802, 2996, 2224, 2224, 2996, 8802, 34236, 9072, 5632, 8136, 5632, 9072, 34236, 133974, 27656, 14416, 21984, 21984, 14416, 27656, 133974, 525636, 84152, 40032, 74080, 86152

Offset

1,1

Comments

Table starts

.....14....45....162....594....2268.....8802.....34236.....133974......525636

.....45...130....336....992....2996.....9072.....27656......84152......256416

....162...336....760...2224....5632....14416.....40032.....101376......259488

....594...992...2224...8136...21984....74080....274320.....747456.....2518720

...2268..2996...5632..21984...86152...359424...1435584....5673232....23721984

...8802..9072..14416..74080..359424..1764000...9438912...46540800...228988224

..34236.27656..40032.274320.1435584..9438912..68074272..366583680..2427719040

.133974.84152.101376.747456.5673232.46540800.366583680.2870491680.23806365696

Links

R. H. Hardin, Table of n, a(n) for n = 1..840

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -a(n-2) +12*a(n-3) -36*a(n-4) for n>5

k=2: a(n) = a(n-1) +6*a(n-2) +4*a(n-3) -10*a(n-4) for n>6

k=3: a(n) = 18*a(n-3) for n>6

k=4: a(n) = 34*a(n-3) for n>7

k=5: a(n) = 66*a(n-3) for n>8

k=6: a(n) = 130*a(n-3) for n>9

k=7: a(n) = 258*a(n-3) for n>10

apparently a(n) = (2^(k+1) +2)*a(n-3) for k>2 and n>k+3

Example

Some solutions for n=4 k=3
..0..1..0..2....0..0..1..2....0..0..1..2....0..0..1..0....0..0..1..1
..1..0..0..2....2..0..0..1....0..1..2..2....0..1..0..0....2..2..0..1
..0..0..1..0....0..2..0..0....1..2..2..0....1..0..0..2....0..2..2..0
..0..2..0..0....0..0..1..0....2..2..0..1....0..0..1..0....1..0..2..2
..2..0..0..1....1..0..0..1....2..0..1..1....0..1..0..0....1..1..0..0

Crossrefs

Sequence in context: A215199 A216258 A064348 * A328243 A369240 A123295

Adjacent sequences: A206212 A206213 A206214 * A206216 A206217 A206218

Keyword

nonn,tabl

Author

R. H. Hardin Feb 04 2012

Status

approved