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A068322
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Number of arithmetic progressions of positive odd integers, strictly increasing with sum n.
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6
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1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 1, 3, 1, 3, 3, 5, 1, 4, 1, 5, 4, 5, 1, 7, 2, 6, 5, 8, 1, 7, 1, 9, 6, 8, 2, 11, 1, 9, 7, 12, 1, 10, 1, 12, 10, 11, 1, 15, 2, 12, 9, 15, 1, 13, 3, 16, 10, 14, 1, 18, 1, 15, 12, 20, 4, 17, 1, 19, 12, 17, 1, 22, 1, 18, 16, 22, 2, 20, 1, 24, 15, 20, 1, 25, 5, 21, 15, 26
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OFFSET
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1,8
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LINKS
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FORMULA
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G.f.: x/(1 - x^2) + Sum_{m >= 2} x^(m^2)/((1 - x^(2*m)) * (1 - x^(m*(m-1))).
(End)
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EXAMPLE
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a(12) = 3 because we have the following arithmetic progressions of odd numbers, strictly increasing with sum n=12: 1+11, 3+9, and 5+7.
a(13) = 1 because we have only the following arithmetic progressions of odd numbers, strictly increasing with sum n=13: 13.
a(14) = 3 because we have the following arithmetic progressions of odd numbers, strictly increasing with sum n=14: 1+13, 3+11, and 5+9.
a(15) = 3 because we have the following arithmetic progressions of odd numbers, strictly increasing with sum n=15: 15, 3+5+7, and 1+5+9.
(End)
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CROSSREFS
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Cf. A049980, A049981, A049982, A049983, A049986, A049987, A049988, A049989, A049990, A068323, A068324, A070211, A127938, A175327, A325328, A325407, A325545, A325546, A325547, A325548.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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