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A160760 Triangle read by rows, binomial transform of an infinite lower triangular Toeplitz matrix with A078008 in every column. 2
1, 1, 1, 3, 2, 1, 9, 5, 3, 1, 27, 14, 8, 4, 1, 81, 41, 22, 12, 5, 1, 243, 122, 63, 34, 17, 6, 1, 729, 365, 185, 97, 51, 23, 7, 1, 2187, 1094, 550, 282, 148, 74, 30, 8, 1, 6561, 3281, 1644, 832, 430, 222, 104, 38, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums = A025192: (1, 2, 6, 18, 54, 162, 486, 1458,...).

A triangle formed like Pascal's triangle, but with 3^n for n>=0 on the left border instead of 1. - Boris Putievskiy, Aug 19 2013

LINKS

Table of n, a(n) for n=0..54.

FORMULA

A007318 * an infinite lower triangular Toeplitz matrix with A078008 in every column: (1, 0, 2, 2, 6, 10, 22, 42, 86,...).

Closed-form formula for arbitrary left and right borders of Pascal like triangle see A228196. - Boris Putievskiy, Aug 19 2013

EXAMPLE

First few rows of the triangle =

1;

1, 1;

3, 2, 1;

9, 5, 3, 1;

27, 14, 8, 4, 1;

81, 41, 22, 12, 5, 1;

243, 122, 63, 34, 17, 6, 1;

729, 365, 185, 97, 51, 23, 7, 1;

2187, 1094, 550, 282, 148, 74, 30, 8, 1;

6561, 3281, 1644, 832, 430, 222, 104, 38, 9, 1;

...

CROSSREFS

Cf. A078008, A025192.

Sequence in context: A156647 A183154 A193791 * A152860 A002350 A109267

Adjacent sequences: A160757 A160758 A160759 * A160761 A160762 A160763

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, May 25 2009

EXTENSIONS

T(7,4) corrected by Georg Fischer, Oct 08 2021

STATUS

approved

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)