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!)
A306489 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of 1/(1 - Sum_{d|k} x^d). 0
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 5, 1, 1, 1, 1, 3, 3, 8, 1, 1, 1, 2, 1, 6, 4, 13, 1, 1, 1, 1, 4, 1, 10, 6, 21, 1, 1, 1, 2, 1, 7, 2, 18, 9, 34, 1, 1, 1, 1, 3, 1, 13, 3, 31, 13, 55, 1, 1, 1, 2, 2, 6, 1, 25, 4, 55, 19, 89, 1, 1, 1, 1, 3, 3, 10, 1, 46, 5, 96, 28, 144, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,9
COMMENTS
A(n,k) is the number of compositions (ordered partitions) of n into divisors of k.
LINKS
FORMULA
G.f. of column k: 1/(1 - Sum_{d|k} x^d).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
1, 2, 1, 2, 1, 2, ...
1, 3, 2, 3, 1, 4, ...
1, 5, 3, 6, 1, 7, ...
1, 8, 4, 10, 2, 13, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[1/(1 - Sum[x^d, {d, Divisors[k]}]), {x, 0, n}]][i - n + 1], {i, 0, 12}, {n, 0, i}] // Flatten
CROSSREFS
Columns k=1..7 give A000012, A000045 (for n > 0), A000930, A060945, A003520, A079958, A005709.
Sequence in context: A371212 A250261 A063669 * A319734 A211005 A162154
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Feb 19 2019
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 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)