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Search: id:A115671
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| A115671 |
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Number of partitions of n into parts not congruent to 0,2,12,14,16,18,20,30 (mod 32). |
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+0
1
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| 1, 1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 34, 44, 56, 72, 91, 114, 143, 178, 220, 272, 334, 408, 498, 605, 732, 884, 1064, 1276, 1528, 1824, 2171, 2580, 3058, 3616, 4269, 5028, 5910, 6936, 8124, 9498, 11088, 12922, 15034, 17468, 20264, 23472, 27154, 31369
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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G. E. Andrews, q-series, CBMS Regional Conference Series in Mathematics, 66, Amer. Math. Soc. 1986, see p. 32. MR0858826 (88b:11063)
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FORMULA
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Euler transform of period 32 sequence [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, ...].
Given g.f. A(x), then B(x)=(2*A(x)-1)^2=g.f. A007096 satisfies 0=f(B(x), B(x^2)) where f(u, v)=1+u^2-2uv^2.
G.f. (1+sqrt(theta_3(x)/theta_4(x)))/2 = (Sum_{k} x^(8k^2-2k))/(Sum_{k} (-x)^(2k^2-k)) = (Sum_{k} x^(24n^2+2n) -x^(24*n^2+14n+2))/(Product_{k>0} 1-x^k).
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (1+eta(x^2+A)^3/eta(x+A)^2/eta(x^4+A))/2, n))}
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CROSSREFS
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Cf. A080054(n)=2a(n) if n>0.
Sequence in context: A035950 A133153 A100673 this_sequence A105782 A035956 A035963
Adjacent sequences: A115668 A115669 A115670 this_sequence A115672 A115673 A115674
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jan 29 2006
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