|
| |
|
|
A100684
|
|
Number of partitions of 2n free of multiples of 8 such that 4 occurs at most once. All odd parts occur with even multiplicities. There is no restriction on the other even parts.
|
|
0
| |
|
|
1, 2, 4, 8, 12, 20, 32, 48, 72, 106, 152, 216, 305, 422, 580, 792, 1068, 1432, 1908, 2520, 3313, 4332, 5628, 7280, 9373, 12008, 15324, 19480, 24661, 31112, 39120, 49016, 61229, 76260, 94692, 117264, 144834, 178412, 219244, 268784, 328746
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| Noureddine Chair, Partition identities from partial supersymmetry.
|
|
|
FORMULA
| G.f.: (1-x^4)*Product((1+x^(2*i))/(1-x^(2*i-1))^2, i=1..infinity). (Jovovic)
Expansion of (1-q^4)q^(-1/6)eta(q^4)eta(q^2)/eta(q)^2 in powers of q.
G.f.: (1-x^4) Prod_{k>0} (1+x^(2k))(1+x^k)^2. - Michael Somos Feb 10 2005
|
|
|
PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (1-x^4)*eta(x^4+A)*eta(x^2+A)/eta(x+A)^2, n))} /* Michael Somos Feb 10 2005 */
|
|
|
CROSSREFS
| Cf. A080054.
Sequence in context: A023598 A173725 A103258 * A131770 A163489 A076651
Adjacent sequences: A100681 A100682 A100683 * A100685 A100686 A100687
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Noureddine Chair (n.chair(AT)rocketmail.com), Jan 27 2005
|
|
|
EXTENSIONS
| Corrected by Vladeta Jovovic, Feb 01 2005
|
| |
|
|
