

A171608


Triangle by columns, T(n,k); (...n, (n+1)) preceded by (n1) zeros, as an infinite lower triangular matrix


5



1, 2, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0
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OFFSET

1,2


COMMENTS

Let the triangle = M as an infinite lower triangular matrix.
.
M * (1, 2, 3,...) = A002620: (1, 2 4, 6, 9, 12, 16, 20,...)
M * (1, 3, 5,...) = A084265: (1, 2, 6, 9, 15, 20, 28, 35,...)
M * (1, 3, 6,...) = A028724: (1, 2, 6, 9, 18, 24, 40, 50, ...)
Lim_{n>inf.} M^n = A171609: (1, 2, 4, 6, 12, 16, 24, 30, ...)


LINKS

Table of n, a(n) for n=1..54.


FORMULA

Triangle by columns, T(n,k); (...n, (n+1)) preceded by (n1) zeros, as an infinite lower triangular matrix


EXAMPLE

First few rows of the triangle =
1;
2, 0;
0, 2, 0;
0, 3, 0, 0;
0, 0, 3, 0, 0;
0, 0, 4, 0, 0, 0;
0, 0, 0, 4, 0, 0, 0;
0, 0, 0, 5, 0, 0, 0, 0;
0, 0, 0, 0, 5, 0, 0, 0, 0;
0, 0, 0, 0, 6, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0;
...


CROSSREFS

Cf. A002620, A084265, A028724, A171608
Sequence in context: A216921 A280285 A033719 * A307985 A024164 A138805
Adjacent sequences: A171605 A171606 A171607 * A171609 A171610 A171611


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Dec 12 2009


STATUS

approved



