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

Author

Gary W. Adamson, May 25 2009

Keywords

• nonn
• tabl

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

Examples

			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.

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

Extensions

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