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A166826 Number of n X 2 1..4 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. 1
0, 4, 49, 219, 666, 1636, 3499, 6783, 12212, 20748, 33637, 52459, 79182, 116220, 166495, 233503, 321384, 434996, 579993, 762907, 991234, 1273524, 1619475, 2040031, 2547484, 3155580, 3879629, 4736619, 5745334, 6926476, 8302791, 9899199 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = (n^6 + 18*n^5 + 100*n^4 - 731*n^2 + 792*n - 180)/180.
Conjectures from Colin Barker, Mar 26 2018: (Start)
G.f.: x^2*(4 + 21*x - 40*x^2 + 22*x^3 - 2*x^4 - x^5) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
EXAMPLE
All solutions for n=3:
...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...2.1...2.1...2.1...2.1
...2.1...2.1...2.2...3.1...3.2...3.2...3.2...3.3...4.2...2.1...2.1...2.2...2.2
...3.4...4.3...4.3...4.2...3.4...4.2...4.4...4.2...4.3...3.4...4.3...3.4...4.3
------
...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1
...2.3...2.3...2.3...2.4...2.4...3.1...3.1...3.1...3.3...3.3...3.3...3.4...3.4
...2.4...4.3...4.4...3.3...3.4...3.4...4.1...4.4...3.4...4.3...4.4...3.4...4.4
------
...2.1...2.1...2.1...2.2...2.2...2.2...2.2...2.2...2.2...3.1...3.1...3.1...3.1
...4.1...4.3...4.3...3.1...3.1...3.1...3.2...3.3...4.1...3.1...3.2...3.2...3.2
...4.3...4.3...4.4...3.4...4.1...4.4...4.1...4.1...4.3...4.2...3.4...4.2...4.4
------
...3.1...3.1...3.1...3.1...3.2...3.2...3.2...3.2...3.3...4.1
...3.3...4.1...4.2...4.2...3.2...3.3...4.1...4.1...4.1...4.2
...4.2...4.2...4.2...4.4...4.1...4.1...4.1...4.4...4.2...4.3
CROSSREFS
Sequence in context: A340662 A041065 A166838 * A295535 A078187 A100256
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 21 2009
STATUS
approved

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Last modified June 21 23:34 EDT 2024. Contains 373560 sequences. (Running on oeis4.)