OFFSET
0,2
COMMENTS
Row 1 of the array (3, 15, 75, 375, ...) = A005053, (3 * 5^n), deleting the "1".
LINKS
Boris Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732 [math.CO], 2012.
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^(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
EXAMPLE
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.
MATHEMATICA
Table[3^(n - k)*5^k, {n, 0, 8}, {k, 0, n}] // Flatten (* Robert G. Wilson v, Jun 06 2006 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 04 2006
EXTENSIONS
More terms from Robert G. Wilson v, Jun 06 2006
STATUS
approved