A131047 (1/2) * (A007318 - A007318^(-1)).

1, 0, 2, 1, 0, 3, 0, 4, 0, 4, 1, 0, 10, 0, 5, 0, 6, 0, 20, 0, 6, 1, 0, 21, 0, 35, 0, 7, 0, 8, 0, 56, 0, 56, 0, 8, 1, 0, 36, 0, 126, 0, 84, 0, 9

Offset

1,3

Comments

Row sums = (1, 2, 4, 8, ...). A131047 * (1,2,3, ...) = A087447 starting (1, 4, 10, 24, 56, ...). A generalized set of analogous triangles: (1/(Q+1)) * (P^Q - 1/P), Q an integer, generates triangles with row sums = powers of (Q+1). Cf. A131048, A131049, A131050, A131051 for triangles having Q = 2,3,4 and 5, respectively.

A007318, Pascal's triangle, = this triangle + A119467, since one triangle = the zeros or masks of the other. - Gary W. Adamson, Jun 12 2007

Links

Table of n, a(n) for n=1..45.

Formula

Let A007318 (Pascal's triangle) = P, then A131047 = (1/2) * (P - 1/P); deleting the right border of zeros.

Example

First few rows of the triangle:
  1;
  0, 2;
  1, 0,  3;
  0, 4,  0,  4;
  1, 0, 10,  0,  5;
  0, 6,  0, 20,  0, 6;
  1, 0, 21,  0, 35, 0, 7;
  ...

Crossrefs

Cf. A131048, A131049, A131050, A131051.

Cf. A119467.

Sequence in context: A123973 A098493 A058560 * A366548 A143714 A004172

Adjacent sequences: A131044 A131045 A131046 * A131048 A131049 A131050

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 12 2007

Status

approved