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A103258
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G.f. = theta_4(0,x^4)/theta_4(0,x).
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1
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1, 2, 4, 8, 12, 20, 32, 48, 72, 106, 152, 216, 304, 420, 576, 784, 1056, 1412, 1876, 2472, 3240, 4224, 5472, 7056, 9056, 11566, 14712, 18640, 23520, 29572, 37056, 46272, 57600, 71488, 88456, 109152, 134332, 164884, 201888, 246608, 300528, 365428, 443392, 536856
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| G.f. for the number of partitions of 2n in which all odd parts occur with multiplicities 2,4 or 6. The even parts appear at most three times. E.g. a(8)=12 because "8=6+2=6+1+1=4+4=4+2+2=4+2+1+1=4+1+1+1+1=3+3+2=3+3+1+1=2+2+2+1+1=2+2+1+1+1+1= 2+1+1+1+1+1+1".
Also the number of partitions of 2n in which the even parts appear with 2 types c, c* and with multiplicity 1. The odd parts with multiplicity 4. E.g. a(6)=8 because we have 6,6*,42,42*,4*2,4*2*,21111,2*1111
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FORMULA
| Expansion of eta(q^2)*eta(q^4)^2/(eta(q)^2 et(q^8)) in powers of q.
Euler transform of period 8 sequence [2, 1, 2, -1, 2, 1, 2, 0, ...]. - Michael Somos Feb 10 2005
G.f. product_{k>0}((1+x^k)^(2)*(1+x^(2(2k-1)))).
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^4+A)^2/eta(x+A)^2/eta(x^8+A), n))} /* Michael Somos Feb 10 2005 */
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CROSSREFS
| Cf. A002448.
Sequence in context: A014557 A023598 A173725 * A100684 A131770 A163489
Adjacent sequences: A103255 A103256 A103257 * A103259 A103260 A103261
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KEYWORD
| nonn
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AUTHOR
| Noureddine Chair (n.chair(AT)rocketmail.com), Jan 27 2005
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