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A058682 a(n) = p(0) + p(1) + ... + p(n) - n - 1, where p = partition numbers, A000041. 5
0, 0, 1, 3, 7, 13, 23, 37, 58, 87, 128, 183, 259, 359, 493, 668, 898, 1194, 1578, 2067, 2693, 3484, 4485, 5739, 7313, 9270, 11705, 14714, 18431, 22995, 28598, 35439, 43787, 53929, 66238, 81120, 99096, 120732, 146746, 177930, 215267, 259849, 313022, 376282 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Number of non-isomorphic rank-2 matroids over S_n.

Starting (1, 3, 7, 13, ...) = row sums of triangle A171239. - Gary W. Adamson, Dec 05 2009

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 501 terms from Muniru A Asiru)

W. M. B. Dukes, Tables of matroids.

W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.

W. M. B. Dukes, The number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004.

W. M. B. Dukes, On the number of matroids on a finite set, Séminaire Lotharingien de Combinatoire 51 (2004), Article B51g.

Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, arXiv:math/0702316 [math.CO], 2007 (see p. 7).

Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, J. Combin. Theory Ser. B 98(2) (2008), 415-431.

Index entries for sequences related to matroids

FORMULA

G.f.: -1/(1 - x)^2 + (1/(1 - x))*Product_{k>=1} 1/(1 - x^k). - Ilya Gutkovskiy, Aug 10 2018

MAPLE

a:= proc(n) option remember; `if`(n<2, 0,

      combinat[numbpart](n)+a(n-1)-1)

    end:

seq(a(n), n=0..50);  # Alois P. Heinz, Oct 10 2019

MATHEMATICA

With[{s = PartitionsP /@ Range[0, 40]}, MapIndexed[Total@ Take[s, First@ #2] - First@ #2 &, s]] (* Michael De Vlieger, Sep 04 2017 *)

PROG

(GAP) List([1..41], n->Sum([1..n-1], k->NrPartitions(k)-1)); # Muniru A Asiru, Aug 10 2018

CROSSREFS

Column k=2 of A053534.

Cf. A000041, A000065 (first differences), A000070.

Cf. A171239. - Gary W. Adamson, Dec 05 2009

Sequence in context: A164787 A131205 A256309 * A081995 A291141 A053599

Adjacent sequences:  A058679 A058680 A058681 * A058683 A058684 A058685

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 30 2000

EXTENSIONS

Name clarified by Ilya Gutkovskiy, Aug 10 2018

STATUS

approved

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Last modified April 17 01:26 EDT 2021. Contains 343051 sequences. (Running on oeis4.)