id:A049982 - OEIS Search Results

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Number of arithmetic progressions of 2 or more positive integers, strictly increasing with sum n.

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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; listen)

	OFFSET	`1,5`
	LINKS	`Graeme McRae, Counting arithmetic sequences whose sum is n`
	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`
	CROSSREFS	`Sequence in context: A126854 A115206 A093653 this_sequence A070167 A141479 A055081` `Adjacent sequences: A049979 A049980 A049981 this_sequence A049983 A049984 A049985`
	KEYWORD	`nonn`
	AUTHOR	`Clark Kimberling (ck6(AT)evansville.edu)`

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Last modified December 5 17:24 EST 2009. Contains 170342 sequences.

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