A206238 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order

15, 60, 60, 310, 256, 310, 1640, 1136, 1136, 1640, 8910, 5728, 4456, 5728, 8910, 51066, 31652, 27168, 27168, 31652, 51066, 294546, 170728, 133392, 283728, 133392, 170728, 294546, 1710184, 943584, 607008, 1236432, 1236432, 607008, 943584, 1710184

Offset

1,1

Comments

Table starts

......15......60......310......1640........8910........51066........294546

......60.....256.....1136......5728.......31652.......170728........943584

.....310....1136.....4456.....27168......133392.......607008.......3503136

....1640....5728....27168....283728.....1236432......9042600......95322432

....8910...31652...133392...1236432....10915392....118573968....1122086640

...51066..170728...607008...9042600...118573968...1448239080...22535636736

..294546..943584..3503136..95322432..1122086640..22535636736..649065145152

.1710184.5175034.17206032.419146392.10022726928.303011941944.8026428934128

Links

R. H. Hardin, Table of n, a(n) for n = 1..544

Formula

Empirical for column k:

k=1: a(n) = 8*a(n-1) -11*a(n-2) +36*a(n-3) -303*a(n-4) +232*a(n-5) +147*a(n-6) +756*a(n-7) for n>8

k=2: a(n) = 3*a(n-1) +20*a(n-2) -14*a(n-3) -133*a(n-4) +95*a(n-5) +123*a(n-6) +9*a(n-7) -102*a(n-8) for n>10

k=3: a(n) = a(n-1) +129*a(n-3) -129*a(n-4) for n>7

k=4: a(n) = a(n-1) +339*a(n-3) -339*a(n-4) for n>8

k=5: a(n) = a(n-1) +921*a(n-3) -921*a(n-4) for n>9

k=6: a(n) = a(n-1) +2571*a(n-3) -2571*a(n-4) for n>10

k=7: a(n) = a(n-1) +7329*a(n-3) -7329*a(n-4) for n>11

k=8: a(n) = a(n-1) +21219*a(n-3) -21219*a(n-4) for n>12

k=9: a(n) = a(n-1) +62121*a(n-3) -62121*a(n-4) for n>13

k=10: a(n) = a(n-1) +183291*a(n-3) -183291*a(n-4) for n>14

k=11: a(n) = a(n-1) +543729*a(n-3) -543729*a(n-4) for n>15

apparently a(n) = a(n-1) +3*A085279(k+1)*a(n-3) -3*A085279(k+1)*a(n-4) for k>2 and n>k+4

Example

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

Crossrefs

Sequence in context: A022287 A288747 A223344 * A064761 A005945 A223337

Adjacent sequences: A206235 A206236 A206237 * A206239 A206240 A206241

Keyword

nonn,tabl

Author

R. H. Hardin Feb 05 2012

Status

approved