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A188557 Number of 6 X n binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally. 2
7, 13, 24, 44, 80, 144, 256, 448, 769, 1291, 2116, 3384, 5282, 8054, 12012, 17548, 25147, 35401, 49024, 66868, 89940, 119420, 156680, 203304, 261109, 332167, 418828, 523744, 649894, 800610, 979604, 1190996, 1439343, 1729669, 2067496, 2458876 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 6 of A188553.
LINKS
FORMULA
Empirical: a(n) = (1/720)*n^6 - (1/80)*n^5 + (17/144)*n^4 - (3/16)*n^3 + (497/360)*n^2 + (17/10)*n + 4.
Conjectures from Colin Barker, Apr 28 2018: (Start)
G.f.: x*(7 - 36*x + 80*x^2 - 96*x^3 + 66*x^4 - 24*x^5 + 4*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
EXAMPLE
Some solutions for 6 X 3:
..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..0....1..1..1....1..1..1....1..1..1....0..0..0
..1..1..1....1..1..1....0..0..0....1..1..1....1..1..1....1..1..1....0..0..0
..1..1..0....1..1..0....0..0..0....1..1..1....1..1..1....1..1..1....0..0..0
..0..0..0....1..0..0....0..0..0....1..1..0....1..1..1....1..1..0....0..0..0
..0..0..0....0..0..0....0..0..0....1..0..0....1..1..1....0..0..0....0..0..0
CROSSREFS
Cf. A188553.
Sequence in context: A228727 A286916 A032690 * A356966 A090992 A259215
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 04 2011
STATUS
approved

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Last modified May 27 02:41 EDT 2024. Contains 372847 sequences. (Running on oeis4.)