A166815 Number of nX2 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 increasing order.

0, 8, 67, 268, 772, 1836, 3843, 7336, 13056, 21984, 35387, 54868, 82420, 120484, 172011, 240528, 330208, 445944, 593427, 779228, 1010884, 1296988, 1647283, 2072760, 2585760, 3200080, 3931083, 4795812, 5813108, 7003732, 8390491, 9998368

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+115*n^4+60*n^3-566*n^2+372*n)/180.

Empirical: G.f.: x^2*(-8-11*x+33*x^2-23*x^3+5*x^4) / (x-1)^7 . - R. J. Mathar, Nov 23 2015

Example

Some solutions for n=4
...1.3...1.1...1.4...1.2...1.3...1.3...1.2...1.2...1.3...1.1...1.2...1.1...1.1
...1.3...1.4...2.4...3.2...1.4...3.3...2.2...3.2...3.3...1.2...1.4...1.1...1.1
...1.4...1.4...2.4...3.3...2.4...3.3...3.3...3.2...4.2...3.3...1.4...1.4...2.3
...2.2...2.3...3.4...4.3...2.4...4.2...3.4...3.4...4.4...4.3...3.3...3.2...2.4
------
...1.2...1.1...1.2...1.2...1.3...2.3...1.3...1.1...2.4...1.2...1.1...1.2...1.1
...2.2...2.2...1.3...1.3...1.4...2.3...1.3...1.2...3.1...1.4...1.3...1.2...1.1
...3.4...3.3...4.3...4.3...1.4...4.1...4.2...3.3...3.3...1.4...1.4...3.2...1.2
...4.4...3.4...4.4...4.3...2.4...4.4...4.4...4.4...3.3...3.4...2.4...3.4...3.4

Crossrefs

Sequence in context: A052669 A076527 A247112 * A166797 A196453 A343091

Adjacent sequences: A166812 A166813 A166814 * A166816 A166817 A166818

Keyword

nonn

Author

R. H. Hardin Oct 21 2009

Status

approved