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Search: id:A112608
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| A112608 |
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Number of representations of n as a sum of a twice a square and three times a triangular number. |
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+0
5
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| 1, 0, 2, 1, 0, 2, 0, 0, 2, 1, 0, 4, 0, 0, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 1, 0, 2, 2, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 3, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 2, 4, 0, 0
(list; graph; listen)
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OFFSET
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0,3
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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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a(n) = d_{1, 3}(8n+3) - d_{2, 3}(8n+3) where d_{a, m}(n) equals the number of divisors of n which are congruent to a mod m.
Euler transform of period 24 sequence [0, 2, 1, -3, 0, 1, 0, -1, 1, 2, 0, -4, 0, 2, 1, -1, 0, 1, 0, -3, 1, 2, 0, -2, ...]. - Michael Somos Jan 01 2006
Expansion of q^(-3/8)*(eta(q^4)^5*eta(q^6)^2)/(eta(q^2)^2*eta(q^3)*eta(q^8)^2) in powers of q.
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EXAMPLE
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a(11) = 4 since we can write 11 = 2*(2)^2 + 3*1 = 2*(-2)^2 + 3*1 = 2*(1)^2 + 3*3 = 2*(-1)^2 + 3*3
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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^4+A)^5*eta(x^6+A)^2/ eta(x^2+A)^2/eta(x^3+A)/eta(x^8)^2, n))} /* Michael Somos Jan 01 2006 */
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CROSSREFS
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A002324(8n+3)=a(n).
Sequence in context: A062154 A110399 A112214 this_sequence A058677 A033762 A129449
Adjacent sequences: A112605 A112606 A112607 this_sequence A112609 A112610 A112611
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KEYWORD
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nonn
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AUTHOR
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James A. Sellers (sellersj(AT)math.psu.edu), Dec 21 2005
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