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A227085 Number of n X 2 binary arrays indicating whether each 2 X 2 subblock of a larger binary array has lexicographically increasing rows and columns, for some larger (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order. 1
4, 12, 29, 62, 122, 225, 393, 655, 1048, 1618, 2421, 3524, 5006, 6959, 9489, 12717, 16780, 21832, 28045, 35610, 44738, 55661, 68633, 83931, 101856, 122734, 146917, 174784, 206742, 243227, 284705, 331673, 384660, 444228, 510973, 585526, 668554 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (5/24)*n^3 + (35/24)*n^2 + (77/60)*n + 1.

Conjectures from Colin Barker, Sep 07 2018: (Start)

G.f.: x*(2 - x)*(2 - 5*x + 6*x^2 - 3*x^3 + x^4) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

EXAMPLE

Some solutions for n=4:

..0..0....1..1....1..0....1..1....0..0....0..0....1..0....0..0....1..0....1..0

..0..0....1..0....0..1....1..0....0..0....0..0....1..0....0..1....0..0....0..0

..0..1....0..0....0..0....0..0....0..0....0..1....0..0....0..1....0..0....0..1

..1..1....0..1....0..1....0..0....0..1....0..1....0..0....0..0....0..0....0..0

CROSSREFS

Column 2 of A227089.

Sequence in context: A086274 A174121 A128563 * A192978 A260546 A062421

Adjacent sequences:  A227082 A227083 A227084 * A227086 A227087 A227088

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 30 2013

STATUS

approved

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Last modified October 28 09:35 EDT 2020. Contains 338052 sequences. (Running on oeis4.)