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

1,1

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

Links

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

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)

Example

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

Crossrefs

Column 1 is A002023(n-1)

Column 2 is A067411(n+1)

Sequence in context: A223751 A228745 A049319 * A237836 A231324 A274557

Adjacent sequences: A203981 A203982 A203983 * A203985 A203986 A203987

Keyword

nonn,tabl

Author

R. H. Hardin Jan 09 2012

Status

approved