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A223982
Number of n X 3 0..3 arrays with rows unimodal and columns nondecreasing.
1
50, 684, 5029, 25410, 99634, 325120, 922768, 2346883, 5462600, 11818092, 24045385, 46430852, 85704412, 152105120, 260790200, 433664645, 701719286, 1107976716, 1711156645, 2590185158, 3849685950, 5626605920, 8098142520, 11491155975
OFFSET
1,1
Column 3 of A223987.
FORMULA
Empirical: a(n) = (353/181440)*n^9 + (5/126)*n^8 + (10571/30240)*n^7 + (251/144)*n^6 + (46793/8640)*n^5 + (1565/144)*n^4 + (159679/11340)*n^3 + (715/63)*n^2 + (6491/1260)*n + 1.
Conjectures from Colin Barker, Aug 25 2018: (Start)
G.f.: x*(50 + 184*x + 439*x^2 - 100*x^3 + 259*x^4 - 210*x^5 + 120*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
(End)
EXAMPLE
Some solutions for n=3:
..0..2..1....0..3..0....0..1..0....2..2..0....0..1..0....1..2..0....0..0..0
..0..3..1....0..3..1....2..2..0....3..2..0....0..1..2....2..2..1....0..1..0
..0..3..1....0..3..1....2..3..2....3..2..2....2..2..3....2..3..3....0..2..1
CROSSREFS
Cf. A223987.
Sequence in context: A052460 A224168 A223859 * A128799 A231835 A206120
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 30 2013
STATUS
approved

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Last modified September 19 21:59 EDT 2024. Contains 376015 sequences. (Running on oeis4.)