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A026905 Partial sums of the partition numbers A000041. 35
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

REFERENCES

Thomas M. A. Fink, Emmanuel Barillot, and Sebastian E. Ahnert, Dynamics of network motifs, http://www.tcm.phy.cam.ac.uk/~tmf20/PUBLICATIONS/dynamics_motifs.pdf, 2006.

LINKS

Table of n, a(n) for n=1..40.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 800

FORMULA

a(n) = A000070(n) - 1, n>=1.

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}]

CROSSREFS

Cf. A000041, A000070, A001477, A206437.

Rows sums of A133737, A137633, A137679.

Sequence in context: A095944 A014284 A118482 * A212147 A066778 A147079

Adjacent sequences:  A026902 A026903 A026904 * A026906 A026907 A026908

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Edited by N. J. A. Sloane, Jun 20 2015

STATUS

approved

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Last modified August 3 04:30 EDT 2015. Contains 260257 sequences.