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A223839
Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
1
4, 16, 48, 118, 255, 503, 926, 1614, 2690, 4318, 6712, 10146, 14965, 21597, 30566, 42506, 58176, 78476, 104464, 137374, 178635, 229891, 293022, 370166, 463742, 576474, 711416, 871978, 1061953, 1285545, 1547398, 1852626, 2206844, 2616200
OFFSET
1,1
COMMENTS
Row 3 of A223838.
LINKS
FORMULA
Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (29/144)*n^4 + (11/48)*n^3 + (1007/360)*n^2 - (37/30)*n + 2.
Conjectures from Colin Barker, Aug 23 2018: (Start)
G.f.: x*(2 - 2*x + x^2)*(2 - 4*x + 5*x^2 - 4*x^3 + 2*x^4) / (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=3:
..1..1..0....0..0..0....0..1..0....1..0..0....1..0..0....0..1..0....0..1..1
..1..1..0....0..1..0....0..1..0....1..1..1....1..1..0....0..1..1....0..1..1
..1..1..1....0..1..0....1..1..0....1..1..1....1..1..0....1..1..1....0..1..1
CROSSREFS
Cf. A223838.
Sequence in context: A261977 A100625 A203248 * A071009 A210066 A131126
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 27 2013
STATUS
approved