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A026905 a(n) = number of sums S of positive integers satisfying S <= n. 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

Jeff Burch points out that this is just the partial sums of the partition numbers.

Row sums of triangle A133737 - Gary W. Adamson, Sep 22 2007

Partial sums of A000041. Alternatively, first differences give A000041. - Jacques ALARDET, Aug 04 2008, Aug 15 2008

Row sums of triangle A137633. - Gary W. Adamson, Jan 31 2008

Equals row sums of triangle A137679. - Gary W. Adamson, Feb 05 2008

More exactly this is the partial sums of the partition numbers of positive integers A000027. 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

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. 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

STATUS

approved

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Last modified November 26 05:57 EST 2014. Contains 250020 sequences.