

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
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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



