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A188559 Number of 8 X n binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally. 2
9, 17, 32, 60, 112, 208, 384, 704, 1280, 2304, 4097, 7181, 12381, 20965, 34831, 56751, 90683, 142163, 218790, 330818, 491870, 719790, 1037650, 1474930, 2068890, 2866154, 3924527, 5315067, 7124435, 9457547, 12440553, 16224169, 20987389 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 8 of A188553.
LINKS
FORMULA
Empirical: a(n) = (1/40320)*n^8 - (1/2016)*n^7 + (19/2880)*n^6 - (7/180)*n^5 + (1247/5760)*n^4 - (85/288)*n^3 + (17911/10080)*n^2 + (1961/840)*n + 5.
Conjectures from Colin Barker, Apr 28 2018: (Start)
G.f.: x*(9 - 64*x + 203*x^2 - 372*x^3 + 430*x^4 - 320*x^5 + 150*x^6 - 40*x^7 + 5*x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)
EXAMPLE
Some solutions for 8 X 3:
..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1
..1..1..1....1..1..0....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1
..1..1..1....1..0..0....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1
..1..1..1....0..0..0....1..1..1....1..1..1....1..1..1....1..1..0....1..1..1
..1..1..1....0..0..0....1..1..1....1..1..1....1..1..1....1..0..0....1..1..0
..1..1..0....0..0..0....1..1..1....1..0..0....1..1..1....0..0..0....1..0..0
..0..0..0....0..0..0....1..1..1....0..0..0....1..1..0....0..0..0....0..0..0
..0..0..0....0..0..0....1..0..0....0..0..0....0..0..0....0..0..0....0..0..0
CROSSREFS
Cf. A188553.
Sequence in context: A285009 A228260 A147459 * A014004 A090994 A164887
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 04 2011
STATUS
approved

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Last modified April 15 05:45 EDT 2024. Contains 371667 sequences. (Running on oeis4.)