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.

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

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n=1..44

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

Adjacent sequences: A166823 A166824 A166825 * A166827 A166828 A166829

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved