login
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
OFFSET
1,1
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jun 30 2013
STATUS
approved