A166813 Number of n X 8 1..2 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 nondecreasing order.

7, 43, 163, 493, 1285, 3001, 6433, 12868, 24308, 43756, 75580, 125968, 203488, 319768, 490312, 735469, 1081573, 1562273, 2220073, 3108103, 4292143, 5852923, 7888723, 10518298, 13884154, 18156202, 23535818, 30260338, 38608018, 48903490, 61523746, 76904683

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = A000581(n+8)-2. - Alois P. Heinz, May 31 2012

From G. C. Greubel, May 24 2016: (Start)

G.f.: 1/(1-x)^9 - (1+x)/(1-x).

E.g.f.: (1/8!)*(-40320 + 322560*x + 564480*x^2 + 376320*x^3 + 117600*x^4 + 18816*x^5 + 1568*x^6 + 64*x^7 + x^8)*exp(x) + 1. (End)

Example

Some solutions for n=4
...1.1.1.1.1.2.2.2...1.1.1.1.1.1.2.2...1.1.1.1.1.1.2.2...1.1.1.1.1.1.2.2
...1.1.1.1.1.2.2.2...1.1.1.2.2.2.2.2...1.1.1.1.1.1.2.2...1.1.1.1.1.2.2.2
...1.2.2.2.2.2.2.2...1.1.1.2.2.2.2.2...1.1.1.2.2.2.2.2...1.1.1.2.2.2.2.2
...1.2.2.2.2.2.2.2...1.1.2.2.2.2.2.2...1.1.2.2.2.2.2.2...1.1.1.2.2.2.2.2
------
...1.1.1.1.1.1.1.1...1.1.1.1.1.1.1.2...1.1.1.1.1.1.1.2...1.1.1.1.1.1.2.2
...1.1.1.1.1.1.1.1...1.1.1.1.1.1.1.2...1.1.1.1.1.2.2.2...1.2.2.2.2.2.2.2
...1.2.2.2.2.2.2.2...1.1.1.1.1.1.1.2...1.1.1.2.2.2.2.2...2.2.2.2.2.2.2.2
...1.2.2.2.2.2.2.2...1.2.2.2.2.2.2.2...1.1.2.2.2.2.2.2...2.2.2.2.2.2.2.2

Maple

a:= n-> binomial(n+8, 8)-2:
seq (a(n), n=1..40);  # Alois P. Heinz, May 31 2012

Mathematica

Table[Binomial[n+8, 8] -2, {n, 1, 100}] (* G. C. Greubel, May 24 2016 *)

Crossrefs

Sequence in context: A201707 A365302 A255314 * A112563 A143569 A351936

Adjacent sequences: A166810 A166811 A166812 * A166814 A166815 A166816

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved