A120027 Triangle, generated from (3^(n-k) * 5^k) table.

1, 3, 5, 9, 15, 25, 27, 45, 75, 125, 81, 135, 225, 375, 625, 243, 405, 675, 1125, 1875, 3125, 729, 1215, 2025, 3375, 5625, 9375, 15625, 2187, 3645, 6075, 10125, 16875, 28125, 46875, 78125, 6561, 10935, 18225, 30375, 50625, 84375, 140625, 234375

Offset: 0

Author

Gary W. Adamson, Jun 04 2006

Keywords

• nonn
• tabl

Comments

Row 1 of the array (3, 15, 75, 375, ...) = A005053, (3 * 5^n), deleting the "1".

Examples

			First few rows of the array:
  1,  5,  25,  125, ...
  3, 15,  75,  375, ...
  9, 45, 225, 1125, ...
First few rows of the triangle are:
   1;
   3,  5;
   9, 15, 25;
  27, 45, 75, 125;
  ...
Example: a(17) = 675 = (3,2) in the array, = 3^3 * 5^2.
		

Links

• Boris Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732 [math.CO], 2012.

Crossrefs

Cf. A005053, A036561, A036565, A036566.

Programs

Mathematica

Table[3^(n - k)*5^k, {n, 0, 8}, {k, 0, n}] // Flatten (* Robert G. Wilson v, Jun 06 2006 *)

Formula

Antidiagonals of the (3^i * 5^j) multiplication table, as an array.

From Boris Putievskiy, Jan 09 2013: (Start)

T(n,k) = 3^(k-1)*5^(n-1) n, k >0 read by antidiagonals.

a(n) = 3^(A004736(n)-1) * 5^(A002260(n)-1), n > 0, or

a(n) = 3^(j-1) * 5^(i-1), n > 0,

where i = n - t*(t+1)/2, j = (t*t + 3*t + 4)/2 - n, t = floor((-1+sqrt(8*n-7))/2). (End)

G.f.: 1/((1 - 3*x)(1 - 5*x*y)). - Ilya Gutkovskiy, Jun 03 2017

Extensions

More terms from Robert G. Wilson v, Jun 06 2006