A141396 Triangle read by rows, antidiagonals of a multiplication table: 3^n * (numbers not multiples of 3).

1, 2, 3, 4, 6, 9, 5, 12, 18, 27, 7, 15, 36, 54, 81, 8, 21, 45, 108, 162, 243, 10, 24, 63, 135, 324, 486, 729, 11, 30, 72, 189, 405, 972, 1458, 2187, 13, 33, 90, 216, 567, 1215, 2916, 4374, 6561, 14, 39, 99, 270, 648, 1701, 3645, 8748, 13122, 19683, 16, 42, 117, 297

Offset

0,2

Comments

Ternary representation of terms in n-th row have n rightmost adjacent zeros.

Row sums = A141397: (1, 5, 19 62, 193, 587, ...).

Links

Ivan Neretin, Table of n, a(n) for n = 0..5049

Formula

Triangle read by rows, descending antidiagonals of the multiplication table: (top row, numbers not multiples of 3); leftmost column, 3^n.

Example

The array begins:
   1,   2,   4,   5,   7, ...
   3,   6,  12,  15,  21, ...
   9,  18,  36,  45,  63, ...
  27,  54, 108, 135, 189, ...
  81, 162, 324, 405, 567, ...
  ...
Descending antidiagonals of the array give
   1;
   2,    3;
   4,    6,    9;
   5,   12,   18,   27;
   7,   15,   36,   54,   81;
   8,   21,   45,  108,  162,  243;
  10,   24,   63,  135,  324,  486,  729;
  11,   30,   72,  189,  405,  972, 1458, 2187;
  ...

Mathematica

Flatten[Table[3^k*Quotient[(3 (m - k) - 1), 2], {m, 0, 10}, {k, 0, m - 1}]] (* Ivan Neretin, Nov 26 2016 *)

Crossrefs

Cf. A001651, A141397.

Sequence in context: A344844 A185290 A363995 * A159849 A098168 A306441

Adjacent sequences: A141393 A141394 A141395 * A141397 A141398 A141399

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 29 2008

Status

approved