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A223952
Number of 5 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.
1
32, 243, 596, 1062, 1821, 3115, 5233, 8564, 13613, 21017, 31561, 46194, 66045, 92439, 126913, 171232, 227405, 297701, 384665, 491134, 620253, 775491, 960657, 1179916, 1437805, 1739249, 2089577, 2494538, 2960317, 3493551, 4101345, 4791288, 5571469
OFFSET
1,1
COMMENTS
Row 5 of A223949.
LINKS
FORMULA
Empirical: a(n) = (2/15)*n^5 + (1/6)*n^4 + (23/6)*n^3 + (89/6)*n^2 + (1501/30)*n + 200 for n>3.
Conjectures from Colin Barker, Aug 24 2018: (Start)
G.f.: x*(32 + 51*x - 382*x^2 + 491*x^3 + 9*x^4 - 348*x^5 + 132*x^6 + 68*x^7 - 37*x^8) / (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>9.
(End)
EXAMPLE
Some solutions for n=3:
..0..1..1....1..1..1....0..0..1....0..0..1....0..0..0....0..0..0....0..1..1
..0..1..1....0..1..1....0..0..1....1..1..1....0..1..1....0..1..1....0..0..1
..0..1..1....0..0..0....0..0..0....0..0..1....0..1..1....0..0..0....0..1..1
..1..1..1....0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..1..1
..0..0..1....0..0..1....0..0..1....0..0..0....0..1..1....0..0..0....1..1..1
CROSSREFS
Cf. A223949.
Sequence in context: A111442 A104782 A186774 * A224136 A250363 A346637
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 29 2013
STATUS
approved