login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A168021 Triangle T(n,k) read by rows in which row n lists the number of partitions of n into parts divisible by k. 16
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.
Also see A168020.
LINKS
FORMULA
T(n,k) = A000041(n/k) if k|n, else T(n,k)=0.
Sum_{k=1..n} T(n, k) = A047968(n).
From G. C. Greubel, Jan 12 2023: (Start)
T(2*n, n) = 2*A000012(n).
T(2*n-1, n+1) = A000007(n-2). (End)
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,
...
MATHEMATICA
T[n_, k_]:= If[IntegerQ[n/k], PartitionsP[n/k], 0];
Table[T[n, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Jan 12 2023 *)
PROG
(SageMath)
def A168021(n, k): return number_of_partitions(n/k) if (n%k)==0 else 0
flatten([[A168021(n, k) for k in range(1, n+1)] for n in range(1, 16)]) # G. C. Greubel, Jan 12 2023
CROSSREFS
Sequence in context: A096798 A158902 A137587 * A137639 A239631 A113288
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)