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%I #19 Nov 21 2013 13:11:19
%S 1,2,4,7,5,8,10,14,15,19,16,20,21,22,27,30,28,33,32,38,37,39,44,45,51,
%T 46,47,54,55,52,59,62,60,64,50,67,72,78,74,68,81,82,80,85,79,87,86,91,
%U 90,94,102,98,103,99,105,100,108,112,110,113,127,128,125,133,118,123
%N First column of the Zorach additive triangle A035312.
%C One can see that (least unused number in rows 1 through n of A035312) ~ A035311(n) ~ 2n. (Asymptotic equality, and the first quantity does not exceed either of the two others.) - _M. F. Hasler_, May 09 2013
%H Reinhard Zumkeller, <a href="/A035311/b035311.txt">Table of n, a(n) for n = 0..1000</a>
%H A. C. Zorach, <a href="http://www.cazort.net/static/triangle.php">Additive triangle</a>
%H <a href="/A035312/a035312_2.hs.txt">Haskell programs for sequences in connection with Zorach additive triangle</a>
%t (* Assuming n <= t(n,1) <= 3n *) uniqueQ[t1_, n_] := (t[n, 1] = t1; Do[t[n, k] = t[n, k-1] + t[n-1, k-1], {k, 2, n}]; n*(n+1)/2 == Length[ Union[ Flatten[ Table[ t[m, k], {m, 1, n}, {k, 1, m}]]]]); t[n_ , 1] := t[n, 1] = Select[ Complement[ Range[n, 3 n], Flatten[ Table[t[m, k], {m, 1, n - 1}, {k, 1, m}]]], uniqueQ[#, n] & , 1][[1]]; Table[t[n, 1], {n, 1, 66}](* _Jean-François Alcover_, Dec 02 2011 *)
%o See link for Haskell program.
%Y Cf. A035312, A035313, A189713, A035358.
%K nonn,easy,nice
%O 0,2
%A _Alex Zorach_
%E More terms from _Christian G. Bower_
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