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A224141
Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
1
7, 22, 49, 92, 155, 242, 357, 504, 687, 910, 1177, 1492, 1859, 2282, 2765, 3312, 3927, 4614, 5377, 6220, 7147, 8162, 9269, 10472, 11775, 13182, 14697, 16324, 18067, 19930, 21917, 24032, 26279, 28662, 31185, 33852, 36667, 39634, 42757, 46040, 49487, 53102
OFFSET
1,1
COMMENTS
Column 3 of A224146.
LINKS
FORMULA
Empirical: a(n) = (2/3)*n^3 + 2*n^2 + (13/3)*n.
Conjectures from Colin Barker, Aug 27 2018: (Start)
G.f.: x*(7 - 6*x + 3*x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
EXAMPLE
Some solutions for n=3:
..0..0..0....0..0..0....0..1..1....0..1..0....0..0..1....0..1..0....0..0..1
..0..0..0....0..0..0....1..1..1....0..1..1....0..0..1....0..1..0....1..1..1
..0..0..1....1..1..1....1..1..1....1..1..1....0..1..1....0..1..0....1..1..1
CROSSREFS
Cf. A224146.
Sequence in context: A288114 A369549 A129109 * A002412 A211652 A211650
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 31 2013
STATUS
approved