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A171370 Sequence generated from Lim:_{n..inf.} M^n, M = an infinite lower triangular matrix with (1,3,3,3,...) in every column, shifted down twice. 3
1, 3, 6, 12, 18, 30, 42, 66, 84, 120, 150, 210, 252, 336, 402, 534, 618, 786, 906, 1146, 1296, 1596, 1806, 2226, 2478, 2982, 3318, 3990, 4392, 5196, 5730, 6798, 7416, 8652, 9438, 11010, 11916, 13728, 14874, 17166, 18462, 21054, 22650, 25842, 27648, 31260 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A000123 can be generated through an analogous procedure replacing (1,3,3,3,...) with (1,2,2,2,...).

A171370 has the property that (1, 3, 6, 12, 18,...) / (1, 3, 3, 3,..) generates an aerated variant: (1, 0, 3, 0, 6, 0, 12,...).

Similarly, given A000123; (1, 2, 4, 6, 10, 14,...) / (1, 2, 2, 2,...) generates an aerated variant: (1, 0, 2, 0, 6, 0, 10,...).

Row sums of the generating triangle = A032766 starting with 1. - Gary W. Adamson, Feb 15 2010

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

Let M = an infinite lower triangular matrix with (1,3,3,3,...) in every column shifted down twice:

1;

3;

3, 1;

3, 3;

3, 3, 1;

3, 3, 3;

...

Sequence A171370 = Lim:_{n..inf.} M^n, the left-shifted vector considered as a sequence.

MAPLE

a:= n-> (Matrix(n+1, (i, j)-> `if`(i=2*j-1, 1,

        `if`(i>2*j-1, 3, 0)))^n)[n+1, 1]:

seq(a(n), n=0..50);  # Alois P. Heinz, Apr 16 2014

CROSSREFS

Cf. A000123.

Cf. A032766. - Gary W. Adamson, Feb 15 2010

Sequence in context: A116958 A242477 A006156 * A061776 A341316 A298029

Adjacent sequences:  A171367 A171368 A171369 * A171371 A171372 A171373

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Dec 06 2009

EXTENSIONS

a(20)-a(45) from Alois P. Heinz, Apr 16 2014

STATUS

approved

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Last modified July 31 01:50 EDT 2021. Contains 346365 sequences. (Running on oeis4.)