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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums = A006356: (1, 3, 6, 14, 31, 70, 157, 353,...).

Sum of n-th 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

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Last modified March 25 22:28 EDT 2019. Contains 321477 sequences. (Running on oeis4.)