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
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Dec 06 2009
EXTENSIONS
a(20)-a(45) from Alois P. Heinz, Apr 16 2014
STATUS
approved