A203826 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements

144, 1296, 1296, 11664, 27216, 11664, 104976, 571536, 571536, 104976, 944784, 12002256, 28005264, 12002256, 944784, 8503056, 252047376, 1372257936, 1372257936, 252047376, 8503056, 76527504, 5292994896, 67240638864

Offset

1,1

Comments

Table starts

.......144..........1296............11664...............104976

......1296.........27216...........571536.............12002256

.....11664........571536.........28005264...........1372257936

....104976......12002256.......1372257936.........157025515248

....944784.....252047376......67240638864.......17968205387664

...8503056....5292994896....3294791304336.....2056114528873776

..76527504..111152892816..161444773912464...235282648691687184

.688747536.2334210749136.7910793921710736.26923572225438510384

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

k=1: a(n) = 16*9^n

k=2: a(n) = 1296*21^(n-1)

k=3: a(n) = 11664*49^(n-1)

k=4: a(n) = 117*a(n-1) -34398*a(n-3) +86436*a(n-4)

k=5: a(n) = 303*a(n-1) -8127*a(n-2) -394891*a(n-3) +4091304*a(n-4) +21176820*a(n-5) -92236816*a(n-6)

k=6: (order 16 recurrence)

k=7: (order 45 recurrence)

Example

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

Crossrefs

Sequence in context: A222349 A133062 A211473 * A261655 A203819 A222515

Adjacent sequences: A203823 A203824 A203825 * A203827 A203828 A203829

Keyword

nonn,tabl

Author

R. H. Hardin Jan 06 2012

Status

approved