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A227329
Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having two adjacent 1's and two adjacent 0's, with rows and columns of the latter in lexicographically nondecreasing order.
1
4, 11, 34, 104, 285, 683, 1469, 2906, 5383, 9457, 15904, 25780, 40493, 61887, 92339, 134870, 193271, 272245, 377566, 516256, 696781, 929267, 1225737, 1600370, 2069783, 2653337, 3373468, 4256044, 5330749, 6631495, 8196863, 10070574
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (1/5040)*n^7 + (1/720)*n^6 + (37/720)*n^5 - (1/144)*n^4 + (283/180)*n^3 - (1259/180)*n^2 + (3019/210)*n - 2 for n>2.
Conjectures from Colin Barker, Sep 08 2018: (Start)
G.f.: x*(4 - 21*x + 58*x^2 - 84*x^3 + 69*x^4 - 43*x^5 + 37*x^6 - 30*x^7 + 13*x^8 - 2*x^9) / (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 x>10.
(End)
EXAMPLE
Some solutions for n=4:
..0..0....0..0....0..0....0..1....0..1....1..0....1..0....0..0....0..0....0..0
..0..1....0..0....1..1....1..0....0..0....0..0....1..0....0..0....1..1....0..1
..0..0....1..1....0..1....1..0....0..0....1..1....0..1....0..0....1..1....0..0
..1..1....1..0....0..1....0..0....0..0....1..1....0..1....1..0....0..0....0..0
CROSSREFS
Column 2 of A227333.
Sequence in context: A060925 A027045 A243781 * A006765 A151272 A112272
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jul 07 2013
STATUS
approved