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Search: id:A027348
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| A027348 |
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Number of partitions of n into distinct odd parts, the least being congruent to 3 mod 4. |
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+0
2
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| 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 2, 3, 2, 2, 2, 4, 4, 3, 4, 6, 5, 5, 6, 8, 8, 7, 9, 11, 11, 10, 12, 15, 16, 15, 18, 21, 21, 21, 24, 28, 30, 29, 33, 38, 39, 40, 44, 51, 53, 54, 60, 67, 70, 72, 79, 89, 93, 96, 105, 116, 121, 126, 136, 150
(list; graph; listen)
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OFFSET
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1,15
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REFERENCES
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S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 41
G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part I, Springer, New York, 2005, MR2135178 (2005m:11001) See p. 235, Entry 9.4.8
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FORMULA
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G.f.: x^3 / (1 - x^4) + x^8 / ((1 - x^2) * (1 - x^8)) + x^15 / ((1 - x^2) * (1 - x^4) * (1 - x^12)) + x^24 / ((1 - x^2) * (1 - x^4) * (1 - x^6) * (1 - x^16)) + ... [Ramanujan] (Michael Somos, Jul 21 2008)
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EXAMPLE
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x^3 + x^7 + x^8 + x^10 + x^11 + x^12 + x^14 + 2*x^15 + 2*x^16 + x^17 + ...
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PROGRAM
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(PARI) {a(n) = if( n<1, 0, polcoeff( sum(k=1, sqrtint(n+1) - 1, x^(k^2 + 2*k) / (1 - x^(4*k)) / prod(j=1, k-1, 1 - x^(2*j), 1 + O(x^(n + 1 - k^2 - 2*k)))), n))} /* Michael Somos Jul 21 2008 */
(PARI) {a(n) = local(A, B); if(n<1, 0, A = partitions(n); sum(k=1, length(A), if( ((B = A[k])[1]) %4 == 3, prod(j=2, length(B), (B[j] > B[j-1]) & ((B[j] - B[j-1])%2 == 0)))))} /* Michael Somos Jul 21 2008 */
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CROSSREFS
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Cf. A143062.
Adjacent sequences: A027345 A027346 A027347 this_sequence A027349 A027350 A027351
Sequence in context: A072781 A046923 A056173 this_sequence A023566 A090970 A091972
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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