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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.

%I A166812 #11 May 24 2016 20:26:20
%S A166812 6,34,118,328,790,1714,3430,6433,11438,19446,31822,50386,77518,116278,
%T A166812 170542,245155,346102,480698,657798,888028,1184038,1560778,2035798,
%U A166812 2629573,3365854,4272046,5379614,6724518,8347678,10295470,12620254,15380935,18643558,22481938
%N 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.
%H A166812 G. C. Greubel, <a href="/A166812/b166812.txt">Table of n, a(n) for n = 1..1000</a>
%F A166812 a(n) = A000580(n+7)-2. - _Alois P. Heinz_, May 31 2012
%F A166812 From _G. C. Greubel_, May 24 2016: (Start)
%F A166812 G.f.: 1/(1 - x)^8 - 2/(1-x).
%F A166812 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)
%e A166812 Some solutions for n=4
%e A166812 ...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
%e A166812 ...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
%e A166812 ...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
%e A166812 ...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
%e A166812 ------
%e A166812 ...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
%e A166812 ...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
%e A166812 ...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
%e A166812 ...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
%p A166812 a:= n-> binomial(n+7,7)-2:
%p A166812 seq(a(n), n=1..50);  # _Alois P. Heinz_, May 31 2012
%t A166812 Table[Binomial[n+7,7] -2, {n, 1, 100}] (* _G. C. Greubel_, May 24 2016 *)
%K A166812 nonn
%O A166812 1,1
%A A166812 _R. H. Hardin_, Oct 21 2009