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%I #20 Nov 24 2015 19:23:45
%S 5,26,82,208,460,922,1714,3001,5003,8006,12374,18562,27130,38758,
%T 54262,74611,100945,134594,177098,230228,296008,376738,475018,593773,
%U 736279,906190,1107566,1344902,1623158,1947790,2324782,2760679,3262621,3838378,4496386,5245784,6096452,7059050,8145058,9366817
%N Number of n X 6 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.
%C This sequence (and A166812, A166813) correspond to k-tuples x with 0<= x(i+1) <= x(i) <= k except (0,0,0..) and (k,k,k...), where x(i) is the index of the first 2 in row i of the array (or 0 if none); the number of those are the binomials minus 2. - _Robert Israel_, Nov 23 2015
%H Robert Israel, <a href="/A166810/b166810.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000579(n+6)-2. - _R. J. Mathar_, Nov 24 2015
%F G.f.: 1 - 2/(1-x) + 1/(1-x)^7. - _Robert Israel_, Nov 24 2015
%e Some solutions for n=4
%e ...1.1.1.1.1.2...1.1.1.1.2.2...1.1.1.1.1.1...1.1.1.1.1.1...1.1.1.1.1.1
%e ...1.1.1.1.1.2...1.1.1.1.2.2...1.1.1.1.1.1...1.1.1.1.1.2...1.1.1.1.1.2
%e ...1.1.1.1.2.2...1.1.1.1.2.2...1.1.1.1.1.2...1.1.1.2.2.2...1.1.1.1.1.2
%e ...1.1.1.2.2.2...1.1.1.1.2.2...1.1.1.1.2.2...2.2.2.2.2.2...1.1.1.1.1.2
%e ------
%e ...1.1.1.1.1.2...1.1.1.2.2.2...1.1.1.1.1.2...1.1.1.1.2.2...1.1.1.1.1.2
%e ...1.1.2.2.2.2...1.1.2.2.2.2...1.1.1.1.2.2...1.1.1.1.2.2...1.1.1.1.1.2
%e ...1.2.2.2.2.2...1.1.2.2.2.2...1.1.1.1.2.2...1.2.2.2.2.2...1.1.2.2.2.2
%e ...1.2.2.2.2.2...1.1.2.2.2.2...1.1.2.2.2.2...1.2.2.2.2.2...1.1.2.2.2.2
%p seq(binomial(n+6,6)-2, n=1..100); # _Robert Israel_, Nov 24 2015
%o (PARI) Vec(1-2/(1-x)+1/(1-x)^7 + O(x^100)) \\ _Altug Alkan_, Nov 24 2015
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 21 2009
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