

A180262


Triangle by rows, generated from a triangle with (1,2,1,1,1,...) in every column.


3



1, 2, 1, 1, 2, 3, 1, 1, 6, 6, 1, 1, 3, 12, 14, 1, 1, 3, 6, 28, 31, 1, 1, 3, 6, 14, 62, 70, 1, 1, 3, 6, 14, 31, 140, 157, 1, 1, 3, 6, 14, 31, 70, 314, 353, 1, 1, 3, 6, 14, 31, 70, 157, 706, 793, 1, 1, 3, 6, 14, 31, 70, 157, 353, 1586, 1782
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OFFSET

0,2


COMMENTS

Row sums = A006356: (1, 3, 6, 14, 31, 70, 157, 353,...).
Sum of nth row terms = rightmost term of next row.


LINKS

Table of n, a(n) for n=0..65.


FORMULA

Let M = an infinite Toeplitz lower triangular matrix with (1,2,1,1,1,..) in
every column. A180262 = M * a diagonalized variant of A006356 such that
the main diagonal = A006356 prefaced with a 1: (1, 1, 3, 6, 14, 31,...) and the
rest zeros.


EXAMPLE

First few rows of the triangle =
.
1;
2, 1;
1, 2, 3;
1, 1, 6, 6;
1, 1, 3, 12, 14;
1, 1, 3, 6, 28, 31;
1, 1, 3, 6, 14, 62, 70;
1, 1, 3, 6, 14, 31, 140, 157;
1, 1, 3, 6, 14, 31, 70, 314, 353;
1, 1, 3, 6, 14, 31, 70, 157, 706, 793;
1, 1, 3, 6, 14, 31, 70, 157, 353, 1586, 1782;
1, 1, 3, 6, 14, 31, 70, 157, 353, 793, 3564, 4004;
1, 1, 3, 6, 14, 31, 70, 157, 353, 793, 1782, 8008, 8997;
1, 1, 3, 6, 14, 31, 70, 157, 353, 793, 1782, 4004, 17994, 20216;
...
Example: row 3 of the triangle = (1, 1, 6, 6) = termwise products of
(1, 1, 2, 1) and (1, 1, 3, 6).


CROSSREFS

Cf. A006356
Sequence in context: A260876 A152650 A184219 * A161789 A109671 A141289
Adjacent sequences: A180259 A180260 A180261 * A180263 A180264 A180265


KEYWORD

nonn,tabf


AUTHOR

Gary W. Adamson, Aug 21 2010


STATUS

approved



