A128179 A097807 * A002260.

1, 0, 2, 1, 0, 3, 0, 2, 0, 4, 1, 0, 3, 0, 5, 0, 2, 0, 4, 0, 6, 1, 0, 3, 0, 5, 0, 7, 0, 2, 0, 4, 0, 6, 0, 8, 1, 0, 3, 0, 5, 0, 7, 0, 9, 0, 2, 0, 4, 0, 6, 0, 8, 0, 10

Offset

1,3

Comments

Row sums = A002620: (1, 2, 4, 6, 9, 12, 16, 20, 25, 30, ...).

General case see A211161. Let B and C be sequences. By b(n) and c(n) denote elements B and C respectively. Table T(n,k) = b(n), if k is odd, c(k) if k is even read by antidiagonals. For this sequence b(n)=n, b(n)=A000027(n), c(n)=0, c(n)=A000004(n). - Boris Putievskiy, Feb 05 2013

Links

Table of n, a(n) for n=1..55.

Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.

Formula

A097807 * A002260 as infinite lower triangular matrices. k-th column = (k, 0, k, 0, ...).

From Boris Putievskiy, Feb 05 2013: (Start)

T(n,k) = (1-(-1)^k)*n/2;

a(n) = (1-(-1)^A004736(n))*A002260(n)/2;

a(n) = (1-(-1)^j)*i/2, where i = n-t*(t+1)/2, j = (t*t+3*t+4)/2-n, t = floor((-1+sqrt(8*n-7))/2). (End)

Example

From Boris Putievskiy, Feb 05 2013: (Start)
The start of the sequence as a table:
  1, 0, 1, 0, 1, 0, 1, ...
  2, 0, 2, 0, 2, 0, 2, ...
  3, 0, 3, 0, 3, 0, 3, ...
  4, 0, 4, 0, 4, 0, 4, ...
  5, 0, 5, 0, 5, 0, 5, ...
  6, 0, 6, 0, 6, 0, 6, ...
  7, 0, 7, 0, 7, 0, 7, ...
  ... (End)
First few rows of the triangle:
  1;
  0, 2;
  1, 0, 3;
  0, 2, 0, 4;
  1, 0, 3, 0, 5;
  0, 2, 0, 4, 0, 6;
  1, 0, 3, 0, 5, 0, 7;
  ...

Crossrefs

Cf. A000004, A000027, A002260, A002620, A004736, A097807, A211161.

Sequence in context: A368464 A143153 A127448 * A356749 A178780 A058558

Adjacent sequences: A128176 A128177 A128178 * A128180 A128181 A128182

Keyword

nonn,tabl

Author

Gary W. Adamson, Feb 17 2007

Status

approved