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A072457 Shadow transform of tetrahedral numbers A000292.

%I A072457 #20 Jan 07 2025 05:57:27
%S A072457 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 A072457 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 A072457 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 A072457 Shadow transform of tetrahedral numbers A000292.
%H A072457 Alois P. Heinz, <a href="/A072457/b072457.txt">Table of n, a(n) for n = 0..10000</a>
%H A072457 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 A072457 OEIS Wiki, <a href="https://oeis.org/wiki/Shadow_transform">Shadow transform</a>.
%H A072457 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%p A072457 a:= n-> add(`if`(modp(j*(j+1)*(j+2)/6, n)=0, 1, 0), j=0..n-1):
%p A072457 seq(a(n), n=0..120);  # _Alois P. Heinz_, Sep 16 2019
%t A072457 a[n_] := Sum[If[Mod[j*(j+1)*(j+2)/6, n] == 0, 1, 0], {j, 0, n-1}];
%t A072457 Table[a[n], {n, 0, 120}] (* _Jean-François Alcover_, Jan 07 2025, after _Alois P. Heinz_ *)
%Y A072457 Cf. A000292.
%K A072457 nonn
%O A072457 0,5
%A A072457 _N. J. A. Sloane_, Aug 02 2002