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A144865 Shadow transform of C(n+3,4) = A000332(n+3).

%I A144865 #10 Sep 16 2019 15:45:25
%S A144865 1,1,1,1,4,1,4,1,2,4,4,1,4,5,6,1,4,3,4,4,5,3,4,1,4,4,2,3,4,5,4,1,5,6,
%T A144865 16,2,4,3,6,4,4,5,4,4,9,5,4,1,4,6,7,2,4,2,16,2,7,4,4,5,4,5,11,1,16,7,
%U A144865 4,7,6,16,4,2,4,4,5,2,16,5,4,4,2,6,4,5,16,3,5,6,4,13,16,3,6,5,16,1,4,6,10,3,4
%N A144865 Shadow transform of C(n+3,4) = A000332(n+3).
%H A144865 Alois P. Heinz, <a href="/A144865/b144865.txt">Table of n, a(n) for n = 1..1000</a>
%H A144865 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 A144865 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%p A144865 shadow:= proc(p) proc(n) local j; add (`if` (modp(p(j), n)=0, 1,0), j=0..n-1) end end: f:= proc(k) proc(n) binomial (n+k-1,k) end end: a:= n-> shadow (f(4))(n): seq (a(n), n=1..120);
%Y A144865 4th column of A144871. Cf. A007318.
%K A144865 nonn
%O A144865 1,5
%A A144865 _Alois P. Heinz_, Sep 23 2008