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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 R. H. Hardin, Table of n, a(n) for n = 1..200 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 Adjacent sequences: A188556 A188557 A188558 * A188560 A188561 A188562 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.)