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%I #12 Apr 05 2018 12:04:57
%S 1,4,10,17,25,34,44,55,67,80,94,109,125,142,160,179,199,220,242,265,
%T 289,314,340,367,395,424,454,485,517,550,584,619,655,692,730,769,809,
%U 850,892,935,979,1024,1070,1117,1165,1214,1264,1315,1367,1420,1474,1529,1585
%N Number of nondecreasing arrangements of n+2 numbers in 0..2 with each number being the sum mod 3 of two others.
%C Column 2 of A183912.
%H R. H. Hardin, <a href="/A183905/b183905.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = (1/2)*n^2 + (7/2)*n - 5 for n>1.
%F a(n) = Triangular number(A000217)-11.
%F Conjectures from _Colin Barker_, Apr 05 2018: (Start)
%F G.f.: x*(1 + x + x^2 - 2*x^3) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
%F (End)
%e Some solutions for n=4:
%e ..0....0....1....0....1....0....0....0....0....0....0....0....1....0....0....0
%e ..1....0....1....1....1....1....0....0....1....0....0....0....1....0....0....0
%e ..2....0....1....1....1....1....0....0....1....1....1....1....2....0....0....0
%e ..2....1....1....1....2....1....1....0....2....2....1....1....2....1....0....2
%e ..2....2....2....2....2....1....1....1....2....2....1....2....2....1....0....2
%e ..2....2....2....2....2....2....1....1....2....2....2....2....2....2....0....2
%t Abs[Table[n (n + 1)/2 - 11, {n, 4, 200}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 12 2011 *)
%Y Cf. A000217, A183912.
%K nonn,easy
%O 1,2
%A _R. H. Hardin_, Jan 07 2011
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