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A174026 Convolved with its aerated variant = (1, 2, 3, ...). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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 + ...).

LINKS

Table of n, a(n) for n=1..98.

FORMULA

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

EXAMPLE

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.

Sequence in context: A256678 A066709 A258051 * A226075 A279226 A108354

Adjacent sequences: A174023 A174024 A174025 * A174027 A174028 A174029

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Mar 06 2010

EXTENSIONS

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

STATUS

approved

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Last modified November 27 00:20 EST 2022. Contains 358362 sequences. (Running on oeis4.)