A144866 Shadow transform of C(n+4,5) = A000389(n+4).

1, 1, 2, 1, 1, 3, 5, 2, 4, 1, 5, 3, 5, 8, 1, 2, 5, 6, 5, 1, 11, 7, 5, 6, 1, 7, 4, 8, 5, 4, 5, 2, 11, 8, 4, 7, 5, 7, 11, 2, 5, 15, 5, 9, 4, 8, 5, 6, 5, 1, 12, 8, 5, 6, 3, 13, 12, 7, 5, 4, 5, 8, 22, 2, 8, 16, 5, 11, 11, 6, 5, 12, 5, 7, 1, 8, 25, 16, 5, 2, 4, 8, 5, 22, 5, 7, 11, 15, 5, 6, 25, 8, 11, 8, 5, 5

Offset: 1

Author

Alois P. Heinz, Sep 23 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• 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

5th 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(5))(n):
seq(a(n), n=1..120);