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Search: id:A097723
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| A097723 |
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One fourth of sum of divisors of 4n+3. |
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+0
7
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| 1, 2, 3, 6, 5, 6, 10, 8, 12, 14, 11, 12, 18, 18, 15, 26, 17, 18, 31, 20, 21, 30, 28, 30, 39, 26, 27, 38, 36, 36, 42, 32, 33, 60, 35, 42, 57, 38, 48, 54, 41, 42, 65, 62, 45, 62, 54, 48, 84, 50, 60, 78, 53, 66, 74, 56, 57, 96, 72, 60, 91, 70, 63, 108, 76, 66, 90, 68, 93, 104, 71, 84, 98
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 76, Eq. (31.54).
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FORMULA
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Euler transform of period 4 sequence [2, 0, 2, -4, ...]. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 14 2004
Expansion of q^(-3/4)eta^2(q^2)eta^4(q^4)/eta^2(q) in powers of q. - Michael Somos Jul 05 2006
Expansion of q^(-3/2)(theta_2(q)theta_2(q^2))^2/16 in powers of q^2. - Michael Somos Jul 05 2006
Expansion of (psi(q)psi(q^2))^2 in powers of q where psi() is a Ramanujan theta function.
a(n)=sigma(4n+3)/4.
a(n)=number of solutions of 8n+6=x^2+y^2+2z^2+2w^2 in positive odd integers.
a(n)=number of representations of n as the sum of two triangular numbers and twice two triangular numbers. - Michael Somos Jul 05 2006
G.f.: (Product_{n>0} (1-q^4n)^2/(1-q^(2n-1)))^2.
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PROGRAM
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(PARI) a(n)=if(n<0, 0, sigma(4*n+3)/4) /* Michael Somos Jul 05 2006 */
(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, n))} /* Michael Somos Jul 05 2006 */
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CROSSREFS
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Cf. A033686.
Adjacent sequences: A097720 A097721 A097722 this_sequence A097724 A097725 A097726
Sequence in context: A142151 A003968 A076734 this_sequence A087786 A080950 A023852
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KEYWORD
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nonn
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AUTHOR
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njas, Sep 11 2004
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