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A049982
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Number of arithmetic progressions of 2 or more positive integers, strictly increasing with sum n.
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1
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0, 0, 1, 1, 2, 3, 3, 3, 6, 5, 5, 8, 6, 7, 12, 8, 8, 14, 9, 11, 17, 12, 11, 19, 14, 14, 22, 16, 14, 27, 15, 17, 27, 19, 21, 32, 18, 21, 32, 25, 20, 38, 21, 25, 42, 26, 23, 42, 26, 32, 43, 30, 26, 49, 33, 33, 48, 33, 29, 59, 30, 35, 56, 37, 39
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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LINKS
| Graeme McRae, Counting arithmetic sequences whose sum is n
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FORMULA
| a(n) has generating function x^3/(x^3-x-x^2+1) + x^6/(x^6-x^3-x^3+1) + x^10/(x^10-x^6-x^4+1) + ... which is the sum k=2,3,... of x^t(k)/(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 positive integers, strictly increasing with sum n. - Graeme McRae (g_m(AT)mcraefamily.com), Feb 08 2007
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CROSSREFS
| Sequence in context: A115206 A093653 A205442 * A070167 A168113 A170895
Adjacent sequences: A049979 A049980 A049981 * A049983 A049984 A049985
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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