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A166842
Number of n X 3 1..3 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in decreasing order.
0
1, 14, 78, 284, 807, 1946, 4172, 8184, 14973, 25894, 42746, 67860, 104195, 155442, 226136, 321776, 448953, 615486, 830566, 1104908, 1450911
OFFSET
1,2
FORMULA
Empirical: a(n) = (1/90)*n*(n^5 + 9*n^4 + 40*n^3 + 30*n^2 + 4*n + 6).
From G. C. Greubel, May 25 2016: (Start)
Empirical G.f.: x*(1 + 7*x + x^2 - 3*x^3 + 2*x^4)/(1 - x)^7.
Empirical E.g.f.: (1/90)*x*(90 + 540*x + 585*x^2 + 195*x^3 + 24*x^4 + x^5)*exp(x). (End)
EXAMPLE
Some solutions for n=4:
...3.1.1...3.2.1...3.1.1...2.1.1...2.1.1...2.1.1...2.2.1...3.1.1...1.1.1
...3.3.1...3.2.2...3.2.1...2.2.1...2.2.1...3.3.1...3.2.2...3.1.1...3.2.1
...3.3.1...3.2.2...3.3.1...3.1.1...3.2.1...3.3.1...3.3.2...3.2.2...3.3.3
...3.3.2...3.3.2...3.3.3...3.3.3...3.3.1...3.3.1...3.3.3...3.3.2...3.3.3
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...2.2.1...1.1.1...1.1.1...1.1.1...3.1.1...3.2.2...2.2.1...2.1.1...1.1.1
...3.2.2...1.1.1...3.2.1...3.2.1...3.1.1...3.2.2...3.2.1...2.1.1...2.1.1
...3.3.3...3.2.1...3.2.1...3.2.3...3.2.1...3.2.2...3.3.1...2.2.1...3.3.1
...3.3.3...3.3.1...3.2.2...3.3.3...3.2.2...3.3.1...3.3.1...3.1.1...3.3.1
CROSSREFS
Sequence in context: A044201 A044582 A058895 * A364770 A370960 A231241
KEYWORD
nonn,more
AUTHOR
R. H. Hardin, Oct 21 2009
STATUS
approved