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Search: id:A033761
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| A033761 |
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Product t2(q^d); d | 2, where t2 = theta2(q)/(2*q^(1/4)). |
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+0
4
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| 1, 1, 1, 2, 0, 1, 2, 1, 1, 1, 1, 0, 3, 1, 0, 2, 1, 1, 1, 0, 1, 3, 1, 2, 0, 0, 1, 2, 1, 0, 3, 1, 0, 2, 1, 1, 2, 0, 1, 0, 2, 1, 2, 1, 0, 3, 0, 1, 3, 0, 0, 2, 1, 0, 0, 1, 2, 4, 1, 1, 0, 1, 1, 1, 0, 1, 3, 1, 1, 0, 1, 1, 2, 1, 0, 3, 0, 1, 4, 0, 1, 0, 1, 0, 2, 1, 1, 2, 0, 0, 2, 2, 1, 3, 0, 0, 2, 2, 1, 0, 2, 1, 0, 1, 0
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Also the number of representations of n as the sum of a triangular number and twice a triangular number. - James A. Sellers (sellersj(AT)math.psu.edu), Dec 21 2005
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REFERENCES
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M. D. Hirschhorn, The number of representations of a number by various forms, Discrete Mathematics 298 (2005), 205-211.
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FORMULA
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Euler transform of period 4 sequence [1, 0, 1, -2, ...]. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 14 2004
Expansion of q^(-3/8)eta(q^2)eta^2(q^4)/eta(q) in powers of q. - Michael Somos Jul 05 2006
Expansion of q^(-3/4)(theta_2(q)theta_2(q^2))/4 in powers of q^2. - Michael Somos Jul 05 2006
Expansion of psi(q)psi(q^2) in powers of q where psi() is a Ramanujan theta function.
Given g.f. A(x), then B(x)=x^3*A(x^8) satisfies 0=f(B(x), B(x^2), B(x^3), B(x^6)) where f(u1, u2, u3, u6) = +u1^4*u6^2 +3*u2^2*u3^4 -4*u1*u2*u3*u6*(u2^2 +3*u6^2) - Michael Somos Jul 05 2006
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PROGRAM
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(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), n))} /* Michael Somos Jul 05 2006 */
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CROSSREFS
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Cf. A097723.
Sequence in context: A085097 A117997 A079684 this_sequence A033805 A033797 A033793
Adjacent sequences: A033758 A033759 A033760 this_sequence A033762 A033763 A033764
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 14 2004
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