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A127938
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Number of arithmetic progressions of 2 or more nonnegative integers, strictly increasing with sum n.
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0
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1, 1, 3, 2, 3, 6, 4, 4, 8, 7, 6, 11, 7, 8, 15, 9, 9, 17, 10, 13, 20, 13, 12, 22, 15, 15, 24, 18, 15, 32, 16, 18, 29, 20, 22, 36, 19, 22, 34, 27, 21, 42, 22, 26, 46, 27, 24, 45, 27, 34, 45, 31, 27, 52, 35, 35, 50, 34, 30, 64, 31, 36, 59, 38, 40, 65, 34, 40, 60, 51, 36, 71, 37, 43
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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LINKS
| Graeme McRae, Counting arithmetic sequences whose sum is n
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FORMULA
| G.f.: x/(x^3-x-x^2+1) + x^3/(x^6-x^3-x^3+1) + x^6/(x^10-x^6-x^4+1) + ... which is the sum k=2,3,... of x^{t(k-1)}/(x^{t(k)}-x^{t(k-1)}-x^k+1), where t(k) is the k-th triangular number. Term k of this generating function generates the number of arithmetic progressions of k nonnegative integers, strictly increasing with sum n.
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EXAMPLE
| a(10)=7 because there are five 2-element arithmetic progressions that sum to 10, as well as 1+2+3+4 and 0+1+2+3+4.
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CROSSREFS
| Cf. A049982.
Sequence in context: A113128 A130459 A144216 * A131990 A033771 A033795
Adjacent sequences: A127935 A127936 A127937 * A127939 A127940 A127941
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KEYWORD
| nonn
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AUTHOR
| Graeme McRae (g_m(AT)mcraefamily.com), Feb 08 2007
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