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%I #20 Feb 21 2022 10:18:07
%S 2,3,5,6,7,8,9,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,
%T 30,31,32,33,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
%U 54,55,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78
%N Numbers not of the form m*(m+1)*(m+2)/6, the non-tetrahedral numbers.
%C Complement of A000292; A000040 is a subsequence.
%H G. C. Greubel, <a href="/A145397/b145397.txt">Table of n, a(n) for n = 1..5000</a>
%H Cristinel Mortici, <a href="http://www.fq.math.ca/Papers1/48-4/Mortici.pdf">Remarks on Complementary Sequences</a>, Fibonacci Quart. 48 (2010), no. 4, 343-347.
%F A014306(a(n)) = 1; A023533(a(n)) = 0.
%t Select[Range[100], Binomial[Floor[Surd[6*# -1, 3]] +2, 3] != # &] (* _G. C. Greubel_, Feb 20 2022 *)
%o (PARI) is(n)=binomial(sqrtnint(6*n,3)+2,3)!=n \\ _Charles R Greathouse IV_, Feb 22 2017
%o (Magma) [n: n in [1..100] | Binomial(Floor((6*n-1)^(1/3))+2, 3) ne n ]; // _G. C. Greubel_, Feb 20 2022
%o (Sage) [n for n in (1..100) if binomial( floor( real_nth_root(6*n-1, 3) ) +2, 3) != n ] # _G. C. Greubel_, Feb 20 2022
%Y Cf. A000040, A000292, A014306, A023533.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Oct 14 2008
%E Definition corrected by _Ant King_, Sep 20 2012
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