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
Keywords
Examples
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
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
Programs
-
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 *)
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)