

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
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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,...).
Closedform 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



