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A223632
Number of n X 3 0..1 arrays with rows, antidiagonals and columns unimodal.
1
7, 49, 229, 801, 2297, 5699, 12657, 25753, 48811, 87253, 148501, 242425, 381837, 583031, 866369, 1256913, 1785103, 2487481, 3407461, 4596145, 6113185, 8027691, 10419185, 13378601, 17009331, 21428317, 26767189, 33173449, 40811701, 49864927
OFFSET
1,1
COMMENTS
Column 3 of A223637.
LINKS
FORMULA
Empirical: a(n) = (23/360)*n^6 + (11/120)*n^5 + (91/72)*n^4 + (11/8)*n^3 + (301/180)*n^2 + (23/15)*n + 1.
Conjectures from Colin Barker, Aug 21 2018: (Start)
G.f.: x*(7 + 33*x^2 - 18*x^3 + 29*x^4 - 6*x^5 + x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
EXAMPLE
Some solutions for n=4:
..0..0..1....1..1..0....0..0..0....1..1..0....0..1..0....0..1..0....1..1..0
..1..0..0....0..1..1....0..0..0....1..1..0....1..1..0....0..1..1....0..1..0
..0..1..0....0..1..0....1..0..0....1..1..0....0..0..1....1..1..1....0..0..0
..0..1..0....0..1..0....1..1..1....1..1..0....0..0..1....1..1..0....0..0..0
CROSSREFS
Cf. A223637.
Sequence in context: A188689 A188852 A188845 * A188502 A188517 A206878
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 24 2013
STATUS
approved