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A173305 Triangle by columns, A000009 in every column shifted down twice for k>0. 3
1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 2, 1, 4, 2, 1, 1, 5, 3, 2, 1, 6, 4, 2, 1, 1, 8, 5, 3, 2, 1, 10, 6, 4, 2, 1, 1, 12, 8, 5, 3, 2, 1, 15, 10, 6, 4, 2, 1, 1, 18, 12, 8, 5, 3, 2, 1, 22, 15, 10, 6, 4, 2, 1, 1, 27, 18, 12, 8, 5, 3, 2, 1, 32, 22, 15, 10, 6, 4, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums = A038348

Let the triangle = M. Lim_{n->inf} M^n = the partition numbers, A000041;

equivalent to the statement A000009(x) = A000041(x)/A000041(x^2) or;

(1 + x + x^2 + 2x^3 + 2x^4 +3x^5 + 4x^6 + ...) = (1 + x + 2x^2 + 3x^3 + ...)/

(1 + x^2 + 2x^4 + 3x^6 + 5x^8 + 7x^10 + ...).

LINKS

Table of n, a(n) for n=0..80.

FORMULA

Triangle by columns, A000009 in every column shifted down twice for k>0

EXAMPLE

First few rows of the triangle =

1;

1;

1, 1;

2, 1;

2, 1, 1;

3, 2, 1;

4, 2, 1, 1;

5, 3, 2, 1;

6, 4, 2, 1, 1;

8, 5, 3, 2, 1;

10, 6, 4, 2, 1, 1;

12, 8, 5, 3, 2, 1;

15, 10, 6, 4, 2, 1, 1;

18, 12, 8, 5, 3, 2, 1;

22, 15, 10, 6, 4, 2, 1, 1;

27, 18, 12, 8, 5, 3, 2, 1;

32, 22, 15, 10, 6, 4, 2, 1, 1;

38, 27, 18, 12, 8, 5, 3, 2, 1;

46, 32, 22, 15, 10, 6, 4, 2, 1, 1;

54, 38, 27, 18, 12, 8, 5, 3, 2, 1;

...

CROSSREFS

Cf. A173306, A038348, A000009, A000041

Sequence in context: A129264 A135840 A228570 * A233867 A319814 A220272

Adjacent sequences:  A173302 A173303 A173304 * A173306 A173307 A173308

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Feb 15 2010

STATUS

approved

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Last modified November 11 15:51 EST 2019. Contains 329019 sequences. (Running on oeis4.)