A160760 Triangle read by rows, binomial transform of an infinite lower triangular Toeplitz matrix with A078008 in every column.

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

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