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.

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

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 A356020 A341316

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