|
| |
|
|
A100926
|
|
Number of partitions of n into parts free of odd squares and the only number with multiplicity in the unrestricted partitions is the number 2.
|
|
2
| |
|
|
1, 0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 23, 27, 33, 40, 48, 57, 69, 81, 97, 113, 134, 157, 184, 214, 250, 290, 337, 389, 451, 519, 598, 688, 789, 904, 1035, 1181, 1348, 1535, 1746, 1983, 2250, 2549, 2885, 3261, 3682, 4154, 4680, 5268, 5923, 6656, 7468
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
COMMENTS
| This is also the inverted graded generating function for the number of partitions in which no square parts are present
|
|
|
REFERENCES
| Noureddine Chair, Partition Identities From Partial Supersymmetry, hep-th/0409011 2004.
J. A. Sellers, Journal of Integer Sequences, 7 (2004) Article 04.2.4
|
|
|
FORMULA
| G.f.:=product_{k.0}(1+x^k)/(1-(-1)^k*x^k^2).
|
|
|
EXAMPLE
| E.g."a(10)=8 because 10=8+2=7+3=6+4=5+3+2=6+2+2=4+2+2+2=2+2+2+2+2."
|
|
|
MAPLE
| series(product((1+x^k)/(1-(-1)^k*x^(k^2)), k=1..100), x=0, 100);
|
|
|
CROSSREFS
| Sequence in context: A081360 A117409 A092833 * A179241 A157046 A017979
Adjacent sequences: A100923 A100924 A100925 * A100927 A100928 A100929
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Noureddine Chair (n.chair(AT)rocketmail.com), Nov 22 2004
|
| |
|
|
