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A224040
Number of 4 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
1
16, 55, 105, 168, 252, 363, 508, 695, 933, 1232, 1603, 2058, 2610, 3273, 4062, 4993, 6083, 7350, 8813, 10492, 12408, 14583, 17040, 19803, 22897, 26348, 30183, 34430, 39118, 44277, 49938, 56133, 62895, 70258, 78257, 86928, 96308, 106435, 117348
OFFSET
1,1
COMMENTS
Row 4 of A224038.
LINKS
FORMULA
Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (83/24)*n^2 + (89/4)*n - 3 for n>2.
Conjectures from Colin Barker, Aug 26 2018: (Start)
G.f.: x*(16 - 25*x - 10*x^2 + 33*x^3 - 8*x^4 - 8*x^5 + 3*x^6) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7.
(End)
EXAMPLE
Some solutions for n=3:
..1..1..1....1..1..1....0..0..1....0..1..1....0..0..1....0..0..0....1..1..1
..1..1..1....0..1..1....1..1..1....0..1..1....1..1..1....0..0..1....0..1..1
..1..1..1....0..1..1....0..1..1....0..1..1....1..1..1....1..1..1....0..0..1
..0..1..1....0..1..1....0..0..1....0..0..1....1..1..1....0..1..1....0..0..1
CROSSREFS
Cf. A224038.
Sequence in context: A297842 A172190 A122658 * A244805 A362039 A188838
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 30 2013
STATUS
approved