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A166831
Number of nX3 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 nonincreasing order.
0
1, 26, 129, 419, 1093, 2476, 5069, 9605, 17113, 28990, 47081, 73767, 112061, 165712, 239317, 338441, 469745, 641122, 861841, 1142699, 1496181
OFFSET
1,2
FORMULA
Empirical: a(n) = (1/90)*(n^6 + 9*n^5 + 55*n^4 + 150*n^3 + 124*n^2 - 339*n + 90).
From G. C. Greubel, May 25 2016: (Start)
Empirical G.f.: (1 - 6*x + 40*x^2 - 67*x^3 + 62*x^4 - 27*x^5 + 5*x^6)/(1 - x)^7 - 1.
Empirical E.g.f.: (1/90)*(90 + 1125*x^2 + 795*x^3 + 210*x^4 + 24*x^5 + x^6) - 1. (End)
EXAMPLE
Some solutions for n=4
...2.2.2...1.1.1...2.2.1...3.2.1...2.1.1...2.2.2...1.1.1...1.1.1...2.1.1
...2.2.2...2.2.1...3.2.2...3.2.1...2.2.1...2.2.2...2.2.2...3.2.1...2.1.1
...3.2.1...3.3.3...3.2.2...3.3.1...2.2.2...2.2.2...3.3.2...3.2.2...2.1.1
...3.2.2...3.3.3...3.2.2...3.3.3...3.3.2...3.3.1...3.3.2...3.3.3...2.3.1
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...3.2.1...1.1.1...2.2.1...2.1.1...2.1.1...3.1.1...1.1.1...2.1.1...1.1.1
...3.2.1...2.1.1...2.2.1...3.1.1...2.2.2...3.3.1...2.1.1...2.1.1...2.2.1
...3.2.2...2.2.2...3.1.1...3.3.3...2.2.2...3.3.2...2.3.3...2.2.1...3.1.1
...3.3.3...3.2.2...3.3.1...3.3.3...3.3.2...3.3.2...2.3.3...3.2.1...3.3.1
CROSSREFS
Sequence in context: A304834 A304169 A356535 * A287992 A042316 A042318
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 21 2009
STATUS
approved