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A128179 A097807 * A002260. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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]

FORMULA

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

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). - Boris Putievskiy, Feb 05 2013

EXAMPLE

From Boris Putievskiy, Feb 05 2013: (Start)

The start of the sequence as 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 are:

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: A014405 A143153 A127448 * A178780 A058558 A210869

Adjacent sequences:  A128176 A128177 A128178 * A128180 A128181 A128182

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Feb 17 2007

STATUS

approved

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Last modified January 16 14:39 EST 2022. Contains 350376 sequences. (Running on oeis4.)