A166812 Number of n X 7 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.

6, 34, 118, 328, 790, 1714, 3430, 6433, 11438, 19446, 31822, 50386, 77518, 116278, 170542, 245155, 346102, 480698, 657798, 888028, 1184038, 1560778, 2035798, 2629573, 3365854, 4272046, 5379614, 6724518, 8347678, 10295470, 12620254, 15380935, 18643558, 22481938

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = A000580(n+7)-2. - Alois P. Heinz, May 31 2012

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

G.f.: 1/(1 - x)^8 - 2/(1-x).

E.g.f.: (1/7!)*(-5040 + 35280*x + 52920*x^2 + 29400*x^3 + 7350*x^4 + 882*x^5 + 49*x^6 + x^7)*exp(x). (End)

Example

Some solutions for n=4
...1.1.1.1.2.2.2...1.1.1.1.2.2.2...1.1.1.1.1.1.1...1.1.1.1.1.1.2
...1.1.1.2.2.2.2...1.1.2.2.2.2.2...1.1.1.1.2.2.2...1.1.1.1.1.1.2
...1.2.2.2.2.2.2...1.1.2.2.2.2.2...1.1.2.2.2.2.2...1.1.1.2.2.2.2
...1.2.2.2.2.2.2...1.2.2.2.2.2.2...1.2.2.2.2.2.2...1.2.2.2.2.2.2
------
...1.1.1.1.1.1.2...1.1.1.1.1.1.2...1.1.1.1.1.2.2...1.1.1.1.1.2.2
...1.1.1.2.2.2.2...1.1.1.1.1.2.2...1.1.1.1.1.2.2...1.1.1.2.2.2.2
...1.1.2.2.2.2.2...1.2.2.2.2.2.2...1.1.1.2.2.2.2...1.2.2.2.2.2.2
...2.2.2.2.2.2.2...2.2.2.2.2.2.2...1.1.1.2.2.2.2...2.2.2.2.2.2.2

Maple

a:= n-> binomial(n+7, 7)-2:
seq(a(n), n=1..50);  # Alois P. Heinz, May 31 2012

Mathematica

Table[Binomial[n+7, 7] -2, {n, 1, 100}] (* G. C. Greubel, May 24 2016 *)

Crossrefs

Essentially column k=7 of A132823.

Sequence in context: A061616 A368757 A222308 * A262844 A166941 A086934

Adjacent sequences: A166809 A166810 A166811 * A166813 A166814 A166815

Keyword

nonn,easy

Author

R. H. Hardin, Oct 21 2009

Status

approved