

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
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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 leftshifted vector considered as a sequence.


MAPLE

a:= n> (Matrix(n+1, (i, j)> `if`(i=2*j1, 1,
`if`(i>2*j1, 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



