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Search: id:A112610
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| A112610 |
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Number of representations of n as a sum of two squares and two triangular numbers. |
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+0
4
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| 1, 6, 13, 14, 18, 32, 31, 30, 48, 38, 42, 78, 57, 54, 80, 62, 84, 96, 74, 96, 121, 108, 90, 128, 98, 102, 192, 110, 114, 182, 133, 156, 176, 160, 138, 192, 180, 150, 234, 158, 192, 288, 183, 174, 240, 182, 228, 320, 194, 198, 272, 252, 240, 288, 256, 252, 403, 230
(list; graph; listen)
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OFFSET
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0,2
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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) = sigma(4n+1) where sigma(n) is the sum of the divisors of n
Euler transform of period 4 sequence [ 6, -8, 6, -4, ...]. - Michael Somos Jul 04 2006
Expansion of q^(-1/4)eta^14(q^2)/(eta^6(q)eta^4(q^4)) in powers of q. - Michael Somos Jul 04 2006
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EXAMPLE
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a(1) = 6 since we can write 1 = 1^2 + 0^2 + 0 + 0 = (-1)^2 + 0^2 + 0 + 0 = 0^2 + 1^2 + 0 + 0 = 0^2 + (-1)^2 + 0 + 0 = 0^2 + 0^2 + 1 + 0 = 0^2 + 0^2 + 0 + 1
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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)^14/eta(x+A)^6/eta(x^4+A)^4, n))} /* Michael Somos Jul 04 2006 */
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CROSSREFS
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Adjacent sequences: A112607 A112608 A112609 this_sequence A112611 A112612 A112613
Sequence in context: A115010 A066826 A031113 this_sequence A100205 A140888 A053753
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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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