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 A026905 Partial sums of the partition numbers A000041 of the positive integers. 38
 1, 3, 6, 11, 18, 29, 44, 66, 96, 138, 194, 271, 372, 507, 683, 914, 1211, 1596, 2086, 2713, 3505, 4507, 5762, 7337, 9295, 11731, 14741, 18459, 23024, 28628, 35470, 43819, 53962, 66272, 81155, 99132, 120769, 146784, 177969, 215307 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equivalently, a(n) = number of sums S of positive integers satisfying S <= n. Equivalently, first differences give A000041. - Jacques ALARDET, Aug 04 2008, Aug 15 2008 For the partial sums of the partitions numbers of nonnegative integers A001477 see A000070. - Omar E. Pol, Nov 12 2011 Also number of parts in all regions of n that contain 1 as a part (Cf. A206437). - Omar E. Pol, Mar 11 2012 Also the number of graph minors of the path graph P_n (not counting the null graph). - Eric W. Weisstein, Apr 29 2022 LINKS Thomas M. A. Fink, Emmanuel Barillot, and Sebastian E. Ahnert, Dynamics of network motifs, 2006. INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 800 FORMULA a(n) = A000070(n) - 1, n >= 1. a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(3/2)*Pi*sqrt(n)) * (1 + 11*Pi/(24*sqrt(6*n))). - Vaclav Kotesovec, Oct 25 2016 G.f.: -1/(1 - x) + (1/(1 - x))*Product_{k>=1} 1/(1 - x^k). - Ilya Gutkovskiy, Dec 25 2016 MAPLE a:=n->add(numbpart(k), k=1..n): seq(a(n), n=1..40); # Zerinvary Lajos, Jun 01 2008 MATHEMATICA Table[ Sum[ PartitionsP[k], {k, 1, n}], {n, 1, 45}] (* or: *) PartitionsP[Range] // Accumulate (* Jean-François Alcover, Jun 19 2019 *) CoefficientList[Series[(QPochhammer[x] - 1)/(x (x - 1) QPochhammer[x]), {x, 0, 20}], x] (* Eric W. Weisstein, Apr 29 2022 *) CROSSREFS Cf. A000041, A000070, A001477, A026906, A206437. Rows sums of A133737, A137633, A137679. Sequence in context: A014284 A118482 A281689 * A286272 A212147 A066778 Adjacent sequences:  A026902 A026903 A026904 * A026906 A026907 A026908 KEYWORD nonn AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Jun 20 2015 Name clarified by Omar E. Pol, Apr 30 2022 STATUS approved

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Last modified October 6 03:14 EDT 2022. Contains 357261 sequences. (Running on oeis4.)