login
A227252
Number of n X 2 binary arrays indicating whether each 2 X 2 subblock of a larger binary array has lexicographically nondecreasing rows and columns, for some larger (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
1
2, 3, 9, 23, 53, 113, 225, 421, 745, 1255, 2025, 3147, 4733, 6917, 9857, 13737, 18769, 25195, 33289, 43359, 55749, 70841, 89057, 110861, 136761, 167311, 203113, 244819, 293133, 348813, 412673, 485585, 568481, 662355, 768265, 887335, 1020757, 1169793
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (1/60)*n^5 - (1/12)*n^4 + (5/12)*n^3 + (1/12)*n^2 - (13/30)*n + 1 for n>1.
Conjectures from Colin Barker, Sep 07 2018: (Start)
G.f.: x*(2 - 9*x + 21*x^2 - 26*x^3 + 20*x^4 - 7*x^5 + x^6) / (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>7.
(End)
EXAMPLE
Some solutions for n=4:
..1..1....1..1....1..1....1..0....1..0....1..1....1..1....1..1....1..1....1..1
..1..0....1..1....1..0....0..1....0..1....1..1....1..0....1..0....1..1....1..0
..0..1....1..1....1..0....0..1....1..1....1..0....0..1....1..1....1..0....1..0
..0..0....1..0....0..1....1..0....1..1....1..1....1..0....1..1....0..0....0..0
CROSSREFS
Column 2 of A227256.
Sequence in context: A294910 A111240 A298407 * A274495 A299705 A318231
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jul 04 2013
STATUS
approved