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A168021 Triangle T(n,k) read by rows in which row n lists the number of partitions of n into parts divisible by k. 13
1, 2, 1, 3, 0, 1, 5, 2, 0, 1, 7, 0, 0, 0, 1, 11, 3, 2, 0, 0, 1, 15, 0, 0, 0, 0, 0, 1, 22, 5, 0, 2, 0, 0, 0, 1, 30, 0, 3, 0, 0, 0, 0, 0, 1, 42, 7, 0, 0, 2, 0, 0, 0, 0, 1, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 77, 11, 5, 3, 0, 2, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The row-reversed version is A168016; the row sums are A047968.

Also see A168020.

LINKS

Table of n, a(n) for n=1..78.

Omar E. Pol, Illustration of the shell model of partitions (2D and 3D)

Omar E. Pol, Illustration of the shell model of partitions (2D view)

Omar E. Pol, Illustration of the shell model of partitions (3D view)

FORMULA

T(n,k) = A000041(n/k) if k|n, else T(n,k)=0.

EXAMPLE

Triangle begins:

==============================================

...... k: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 11 12

==============================================

n=1 ..... 1,

n=2 ..... 2, 1,

n=3 ..... 3, 0, 1,

n=4 ..... 5, 2, 0, 1,

n=5 ..... 7, 0, 0, 0, 1,

n=6 .... 11, 3, 2, 0, 0, 1,

n=7 .... 15, 0, 0, 0, 0, 0, 1,

n=8 .... 22, 5, 0, 2, 0, 0, 0, 1,

n=9 .... 30, 0, 3, 0, 0, 0, 0, 0, 1,

n=10 ... 42, 7, 0, 0, 2, 0, 0, 0, 0, 1,

n=11 ... 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

n=12 ... 77,11, 5, 3, 0, 2, 0, 0, 0, 0, 0, 1,

...

CROSSREFS

Cf. A000041, A035377, A035444, A135010, A138121, A168020.

Cf. A168016 - A168019. [From Omar E. Pol, Nov 23 2009]

Sequence in context: A096798 A158902 A137587 * A137639 A239631 A113288

Adjacent sequences:  A168018 A168019 A168020 * A168022 A168023 A168024

KEYWORD

easy,nonn,tabl

AUTHOR

Omar E. Pol, Nov 20 2009, Nov 21 2009

EXTENSIONS

Edited by Charles R Greathouse IV, Mar 23 2010

STATUS

approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)