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

Author

R. H. Hardin Feb 05 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

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