A203984 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.

6, 24, 24, 96, 144, 96, 384, 864, 864, 384, 1536, 5184, 7776, 5184, 1536, 6144, 31104, 69984, 69984, 31104, 6144, 24576, 186624, 629856, 956448, 629856, 186624, 24576, 98304, 1119744, 5668704, 13071456, 13071456, 5668704, 1119744, 98304, 393216

Offset: 1

Author

R. H. Hardin Jan 09 2012

Keywords

• nonn
• tabl

Comments

Table starts

.....6......24........96.........384..........1536............6144

....24.....144.......864........5184.........31104..........186624

....96.....864......7776.......69984........629856.........5668704

...384....5184.....69984......956448......13071456.......178855776

..1536...31104....629856....13071456.....271918944......5671161216

..6144..186624...5668704...178855776....5671161216....180709558848

.24576.1119744..51018336..2447270496..118333620576...5764846339584

.98304.6718464.459165024.33489653472.2469841766784.184042295652096

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 1 is A002023(n-1)

Column 2 is A067411(n+1)

Formula

Empirical for column k:

k=1: a(n) = 6*4^(n-1)

k=2: a(n) = 4*6^n

k=3: a(n) = 96*9^(n-1)

k=4: a(n) = 15*a(n-1) -270*a(n-3) +324*a(n-4)

k=5: a(n) = 25*a(n-1) -45*a(n-2) -963*a(n-3) +2025*a(n-4) +3645*a(n-5) -6561*a(n-6)

k=6: (order 15 recurrence)

k=7: (order 45 recurrence)