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%I #9 Apr 16 2014 12:35:51
%S 1,3,6,12,18,30,42,66,84,120,150,210,252,336,402,534,618,786,906,1146,
%T 1296,1596,1806,2226,2478,2982,3318,3990,4392,5196,5730,6798,7416,
%U 8652,9438,11010,11916,13728,14874,17166,18462,21054,22650,25842,27648,31260
%N 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.
%C A000123 can be generated through an analogous procedure replacing (1,3,3,3,...) with (1,2,2,2,...).
%C 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,...).
%C Similarly, given A000123; (1, 2, 4, 6, 10, 14,...) / (1, 2, 2, 2,...) generates an aerated variant: (1, 0, 2, 0, 6, 0, 10,...).
%C Row sums of the generating triangle = A032766 starting with 1. - _Gary W. Adamson_, Feb 15 2010
%H Alois P. Heinz, <a href="/A171370/b171370.txt">Table of n, a(n) for n = 0..200</a>
%F Let M = an infinite lower triangular matrix with (1,3,3,3,...) in every column shifted down twice:
%F 1;
%F 3;
%F 3, 1;
%F 3, 3;
%F 3, 3, 1;
%F 3, 3, 3;
%F ...
%F Sequence A171370 = Lim:_{n..inf.} M^n, the left-shifted vector considered as a sequence.
%p a:= n-> (Matrix(n+1, (i, j)-> `if`(i=2*j-1, 1,
%p `if`(i>2*j-1, 3, 0)))^n)[n+1, 1]:
%p seq(a(n), n=0..50); # _Alois P. Heinz_, Apr 16 2014
%Y Cf. A000123.
%Y Cf. A032766. - _Gary W. Adamson_, Feb 15 2010
%K nonn
%O 0,2
%A _Gary W. Adamson_, Dec 06 2009
%E a(20)-a(45) from _Alois P. Heinz_, Apr 16 2014
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