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A120027 Triangle, generated from (3^(n-k) * 5^k) table. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

T(n,k) = 3^(k-1)*5^(n-1) n, k >0 read by antidiagonals. - Boris Putievskiy, Jan 09 2013

LINKS

Table of n, a(n) for n=0..43.

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.

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]. - Boris Putievskiy, Jan 09 2013

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

EXAMPLE

First few rows of the array are:

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 *)

CROSSREFS

Cf. A005053, A036561, A036565, A036566.

Sequence in context: A057289 A056754 A003593 * A018586 A135342 A029877

Adjacent sequences:  A120024 A120025 A120026 * A120028 A120029 A120030

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jun 04 2006

EXTENSIONS

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

STATUS

approved

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Last modified January 23 20:16 EST 2022. Contains 350515 sequences. (Running on oeis4.)