

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
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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



