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A224159
Number of 3 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.
1
8, 36, 89, 187, 373, 702, 1252, 2130, 3479, 5486, 8391, 12497, 18181, 25906, 36234, 49840, 67527, 90242, 119093, 155367, 200549, 256342, 324688, 407790, 508135, 628518, 772067, 942269, 1142997, 1378538, 1653622, 1973452, 2343735, 2770714
OFFSET
1,1
COMMENTS
Row 3 of A224158.
LINKS
FORMULA
Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (47/144)*n^4 - (3/16)*n^3 + (1111/180)*n^2 - (199/60)*n + 20 for n>2.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(8 - 20*x + 5*x^2 + 40*x^3 - 47*x^4 - 5*x^5 + 41*x^6 - 27*x^7 + 6*x^8) / (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>9.
(End)
EXAMPLE
Some solutions for n=3:
..0..0..1....0..0..1....0..0..0....0..1..0....1..0..0....0..1..1....1..1..0
..1..1..0....1..1..0....0..0..0....1..0..0....0..1..0....1..1..1....1..0..0
..1..1..1....1..1..0....1..0..0....0..1..0....1..0..0....1..1..0....1..1..0
CROSSREFS
Cf. A224158.
Sequence in context: A321778 A009923 A187287 * A321251 A035006 A245360
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 31 2013
STATUS
approved