The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A002031 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A002031

Number of labeled connected digraphs on n nodes where every node has indegree 0 or outdegree 0 and no isolated nodes.
(history; published version)

#52 by R. J. Mathar at Sat Nov 18 14:17:39 EST 2023

STATUS

editing

approved

#51 by R. J. Mathar at Sat Nov 18 13:24:18 EST 2023

NAME

Number of labeled connected digraphs on n nodes where every node has indegree 0 or outdegree 0 and no isolated nodes.

COMMENTS

In- or outdegree zero implies loops are not admitted. Multi-arcs are not admitted. - R. J. Mathar, Nov 18 2023

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approved

editing

#50 by R. J. Mathar at Sat Nov 18 13:03:26 EST 2023

STATUS

editing

approved

#49 by R. J. Mathar at Sat Nov 18 13:03:16 EST 2023

CROSSREFS

Cf. A001831, A001832, A002032, A047863, A052332, A007776 (unlabeled case). Essentially the same as A002027.

STATUS

approved

editing

#48 by Alois P. Heinz at Fri Jan 12 12:37:25 EST 2018

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proposed

approved

#47 by Jean-François Alcover at Fri Jan 12 05:02:32 EST 2018

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editing

proposed

#46 by Jean-François Alcover at Fri Jan 12 05:02:08 EST 2018

MATHEMATICA

max terms = 1817; f[x_] :s = Log[Sum[ aExp[(2^n - 2)*x]*(x^n/n!), {n, 0, maxterms+2}]] + O[x]^(terms+2); coes = Drop[CoefficientList[ Series[ f[x] - Log[ Sum[ Exp[ (2^n-2)*s, x]*(x^n/n!), {n, 0, max}]], {x, Range[0, max}], x]; Table[a[nterms+1], {n, !, 2, 18}] /. First[ Solve[ Thread[ coes == 0]]] (* Jean-François Alcover, Nov 08 2011, after Vladeta Jovovic , updated Jan 12 2018 *)

STATUS

approved

editing

Discussion

Fri Jan 12

05:02

Jean-François Alcover: Simplified Mma coding.

#45 by N. J. A. Sloane at Sun Jun 21 23:47:40 EDT 2015

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proposed

approved

#44 by Michel Marcus at Sun Jun 21 15:44:47 EDT 2015

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editing

proposed

#43 by Michel Marcus at Sun Jun 21 15:44:42 EDT 2015

LINKS

R. C. Read, RE. CM.; Wright, E. M., <a href="http://dx.doi.org/10.4153/CJM-1970-066-1">Colored graphs: A correction and extension</a>, Canad. J. Math. 22 1970 594-596.

STATUS

proposed

editing