proposed

approved

editing

proposed

N. J. A. Sloane, Lorenz Halbeisen and Norbert Hungerbuehler, <a href="https://transformswww.semanticscholar.txtorg/paper/Number-theoretic-aspects-of-a-combinatorial-Halbeisen-Hungerb%C3%BChler/5743ff2f9c14d22d1a9e570d6951a7c9ef79a612">TransformsNumber theoretic aspects of a combinatorial function</a>, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150; see Definition 7 for the shadow transform.

N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.

approved

editing

editing

approved

N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

Alois P. Heinz, <a href="/A144870/b144870.txt">Table of n, a(n) for n = 1..1000</a>

approved

editing

_Alois P. Heinz (heinz(AT)hs-heilbronn.de), _, Sep 23 2008

N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

nonn,new

nonn

N. J. A. Sloane, <a href="http://www.research.att.com/~njas/sequences/transforms.txt">Transforms</a>

nonn,new

nonn

Shadow transform of C(n+8,9) = A000582(n+8).

1, 1, 1, 1, 4, 1, 2, 1, 1, 5, 9, 1, 9, 3, 1, 2, 9, 1, 9, 6, 2, 12, 9, 1, 8, 13, 1, 4, 9, 6, 9, 2, 8, 16, 9, 1, 9, 13, 9, 7, 9, 3, 9, 18, 1, 13, 9, 2, 4, 12, 8, 14, 9, 1, 37, 4, 8, 13, 9, 8, 9, 16, 1, 2, 38, 11, 9, 20, 7, 16, 9, 1, 9, 12, 13, 14, 21, 16, 9, 12, 1, 13, 9, 6, 37, 12, 16, 20, 9, 8, 22, 17

1,5

N. J. A. Sloane, <a href="http://www.research.att.com/~njas/sequences/transforms.txt">Transforms</a>

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(9))(n): seq (a(n), n=1..100);

9th column of A144871. Cf. A007318.

nonn

Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 23 2008

approved