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A184544
Number of (n+2) X 7 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.
1
309, 792, 1627, 3024, 5313, 8989, 14767, 23648, 36997, 56634, 84939, 124972, 180609, 256695, 359215, 495484, 674357, 906460, 1204443, 1583256, 2060449, 2656497, 3395151, 4303816, 5413957, 6761534, 8387467, 10338132, 12665889, 15429643
OFFSET
1,1
COMMENTS
Column 5 of A184548.
LINKS
FORMULA
Empirical: a(n) = (1/5040)*n^7 + (1/120)*n^6 + (53/360)*n^5 + (17/12)*n^4 + (5767/720)*n^3 + (3063/40)*n^2 + (11959/70)*n + 52.
Conjectures from Colin Barker, Apr 13 2018: (Start)
G.f.: x*(309 - 1680*x + 3943*x^2 - 5120*x^3 + 3955*x^4 - 1819*x^5 + 465*x^6 - 52*x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)
EXAMPLE
Some solutions for 4 X 7:
..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..1..1..1..1..1
..0..0..0..0..0..0..1....0..0..0..0..0..1..1....1..1..1..1..1..1..1
..0..0..0..0..0..1..1....0..0..1..1..1..0..0....1..1..1..1..1..1..1
..0..0..0..1..1..1..0....1..1..1..1..1..1..1....1..1..1..1..1..1..1
CROSSREFS
Cf. A184548.
Sequence in context: A121322 A067730 A183627 * A251345 A105841 A127456
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 16 2011
STATUS
approved