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

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, 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, 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

Offset: 1

Author

Alois P. Heinz, Sep 23 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150. (ps, pdf); see Definition 7 for the shadow transform.
• N. J. A. Sloane, Transforms.

Crossrefs

4th column of A144871. Cf. A007318.

Programs

Maple

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);