A227329 - OEIS

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.

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

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OFFSET

1,1

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

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

Adjacent sequences: A227326 A227327 A227328 * A227330 A227331 A227332

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 07 2013

STATUS

approved