A166841 Number of nX2 1..7 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, 0, 0, 714, 10101, 67447, 306568, 1094952, 3307774, 8826726, 21395896, 48023298, 101190323, 202226037, 386323080

Offset

1,4

Links

Table of n, a(n) for n=1..15.

Formula

From G. C. Greubel, May 25 2016: (Start)

Empirical a(n) = (2^5/(12)!)*n*(n-1)*(n-2)*(n-3)*(76188960 - 75467214*n - 2238226*n^2 + 5642142*n^3 + 994614*n^4 + 75084*n^5 + 3141*n^6 + 78*n^7 + n^9).

Empirical G.f.: x^4*(714 + 819*x - 8174*x^2 + 13431*x^3 - 7942*x^4 - 843*x^5 + 3314*x^6 - 1519*x^7 + 232*x^8)/(1 - x)^13.

Empirical E.g.f.: (2^5/(12)!)*x^4*(445321800 + 814676940*x + 364885290*x^2 + 64062900*x^3 + 5660820*x^4 + 283305*x^5 + 8349*x^6 + 138*x^7 + x^8)*exp(x).

(End)

Example

Some solutions for n=4
...2.1...3.1...2.1...3.2...3.2...2.1...2.1...4.1...5.4...3.2...3.1...3.2...3.2
...5.4...4.1...3.4...4.1...4.6...2.3...5.4...5.3...6.1...4.1...5.4...5.5...4.6
...7.3...5.7...5.6...6.6...5.5...4.5...6.3...5.6...6.3...5.1...5.7...6.1...5.1
...7.6...6.2...5.7...7.5...7.1...7.6...7.7...7.2...7.2...6.7...6.2...7.4...5.7
------
...2.1...3.1...3.2...4.1...2.1...2.2...3.1...3.1...4.2...3.2...3.2...2.1...2.1
...5.4...5.2...3.6...5.6...2.4...4.1...3.6...3.7...4.3...3.4...3.4...4.3...2.7
...5.6...5.7...5.1...7.2...5.6...6.5...5.4...4.5...6.1...5.1...6.1...6.6...4.3
...7.3...6.4...7.4...7.3...7.3...7.3...7.2...6.2...7.5...7.6...7.5...7.5...6.5

Crossrefs

Sequence in context: A321493 A260282 A360358 * A166829 A250378 A005467

Adjacent sequences: A166838 A166839 A166840 * A166842 A166843 A166844

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved