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%I #27 May 27 2016 16:06:29
%S 3,13,33,68,124,208,328,493,713,999,1363,1818,2378,3058,3874,4843,
%T 5983,7313,8853,10624,12648,14948,17548,20473,23749,27403,31463,35958,
%U 40918,46374,52358,58903,66043,73813,82249,91388,101268,111928,123408,135749,148993
%N Number of n X 4 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.
%F a(n) = (n^4 + 10*n^3 + 35*n^2 + 50*n - 24)/24.
%F a(n) = (n^2 + 5*n - 2)*(n^2 + 5*n + 12)/24.
%F a(n) = (1/24)*(n+1)*(n+2)*(n+3)*(n+4) - 2. - _Joerg Arndt_, Apr 14 2011
%F G.f.: x*(3-2*x -2*x^2 +3*x^3 -x^4)/(1-x)^5. - _Colin Barker_, Jan 11 2012
%F E.g.f.: (1/24)*(-24 + 96*x + 72*x^2 + 16*x^3 + x^4)*exp(x) + 1. - _G. C. Greubel_, May 27 2016
%e Some solutions for n=4
%e ...1.1.1.1...1.1.1.1...1.1.1.1...1.1.2.2...1.1.1.1...1.1.2.2...1.1.1.2
%e ...1.1.1.1...1.1.2.2...1.1.1.1...1.2.2.2...1.1.1.1...1.1.2.2...1.1.1.2
%e ...1.1.1.1...1.2.2.2...1.1.1.2...1.2.2.2...1.1.2.2...2.2.2.2...1.1.1.2
%e ...2.2.2.2...1.2.2.2...1.1.2.2...2.2.2.2...2.2.2.2...2.2.2.2...1.2.2.2
%e ------
%e ...1.1.1.1...1.1.2.2...1.1.1.1...1.1.1.1...1.1.1.2...1.1.1.1...1.1.2.2
%e ...1.1.1.2...1.1.2.2...1.2.2.2...1.1.1.1...2.2.2.2...1.1.1.2...2.2.2.2
%e ...2.2.2.2...1.1.2.2...1.2.2.2...1.2.2.2...2.2.2.2...1.1.2.2...2.2.2.2
%e ...2.2.2.2...1.1.2.2...2.2.2.2...2.2.2.2...2.2.2.2...1.2.2.2...2.2.2.2
%p a:= n-> binomial(n+4,4)-2:
%p seq(a(n), n=1..50); # _Alois P. Heinz_, May 31 2012
%t q=60;(Transpose[NestList[Accumulate,Range[q],q]]-2)[[5]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 08 2011 *)
%Y Cf. A063258.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 21 2009
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