%I #16 Sep 16 2019 21:25:39
%S 0,1,1,1,2,3,1,3,2,1,4,3,3,3,4,3,2,3,1,3,7,2,4,3,3,3,4,1,7,3,3,3,2,2,
%T 4,9,2,3,4,3,7,3,6,3,7,2,4,3,2,3,4,4,7,3,1,9,7,4,4,3,6,3,4,4,2,9,4,3,
%U 7,3,13,3,2,3,4,2,7,9,4,3,7,1,4,3,8,9,4,2,7,3,4,9,7,3,4,9,3,3,4,3,7,3,3,3,7
%N Shadow transform of tetrahedral numbers A000292.
%H Alois P. Heinz, <a href="/A072457/b072457.txt">Table of n, a(n) for n = 0..10000</a>
%H Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150. (<a href="http://math.berkeley.edu/~halbeis/publications/psf/seq.ps">ps</a>, <a href="http://math.berkeley.edu/~halbeis/publications/pdf/seq.pdf">pdf</a>); see Definition 7 for the shadow transform.
%H OEIS Wiki, <a href="https://oeis.org/wiki/Shadow_transform">Shadow transform</a>.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%p a:= n-> add(`if`(modp(j*(j+1)*(j+2)/6, n)=0, 1, 0), j=0..n-1):
%p seq(a(n), n=0..120); # _Alois P. Heinz_, Sep 16 2019
%Y Cf. A000292.
%K nonn
%O 0,5
%A _N. J. A. Sloane_, Aug 02 2002