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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 9
144, 1296, 1296, 11664, 27216, 11664, 104976, 571536, 571536, 104976, 944784, 12002256, 28005264, 12002256, 944784, 8503056, 252047376, 1372257936, 1372257936, 252047376, 8503056, 76527504, 5292994896, 67240638864 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 5 01:22 EDT 2020. Contains 335457 sequences. (Running on oeis4.)