A174026 Convolved with its aerated variant = (1, 2, 3, ...).

1, 2, 1, 0, 2, 4, 2, 0, 1, 2, 1, 0, 0, 0, 0, 0, 2, 4, 2, 0, 4, 8, 4, 0, 2, 4, 2, 0, 0, 0, 0, 0, 1, 2, 1, 0, 2, 4, 2, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 4, 8, 4, 0, 2, 4, 2, 0, 0, 0, 0, 0, 4, 8, 4, 0, 8, 16, 8, 0, 4, 8, 4, 0, 0, 0, 0, 0, 2, 4

Offset: 1

Author

Gary W. Adamson, Mar 06 2010

Keywords

• nonn

Comments

Equals left border of triangle A174064.

With suitable polcoeff offsets, we obtain: (x * 2x^2 + x^3 + 2x^5) * (1 + 2x^2 + 4x^4 + 2x^8 + 4x^10 + ...) = (x + 2x^2 + 3x^3 + 4x^4 + 5x^5 + ...).

Examples

			First few rows of triangle A174064 = 1, 2, 1, 0, 2, 4, ... = heading terms, multiplied * left border.
  1;
  2,
  1, 2;
  0, 4;
  2, 2, 1;
  4, 0, 2;
  2, 4, 1, 0;
  0, 8, 0, 0;
  1, 4, 2, 0, 2;
  2, 0, 4, 0, 4;
  ...
where each successive column > 1 is shifted down twice, with terms filled in as a product of (1, 2, 1, 0, 2, 4, 2, ...) * (1, 2, 1, 0, 2, 4, 2, ...).
The next term in the series is generated in the ongoing left column, such that leftmost term = (n - sum of row n terms in columns > 1).
For example, a(9) = 1 since the terms to the right of the 1 in row 9 are (4, 2, 0, 2), sum = 8.
		

Crossrefs

Cf. A174064.

Formula

Left border of a multiplication table with columns >1 shifted down twice, with row sums = (1, 2, 3, ...); as shown in triangle A174064.

Extensions

More terms from R. J. Mathar, Mar 18 2010