A002499 -id:A002499 - cp's OEIS frontend

A047833 Erroneous version of A002499.

Original entry on oeis.org

1, 3, 10, 70, 708, 15248, 543520

Offset: 1

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A047834 Another erroneous version of A002499.

Original entry on oeis.org

1, 3, 10, 70, 709, 47960

Offset: 1

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A002500 Number of self-converse relations on n points.

Original entry on oeis.org

1, 2, 8, 44, 436, 7176, 222368, 12376880, 1302871456, 254079924896, 94287450368768, 65986000800656832, 88430997899765949952, 226039101814259861321856, 1112311767839787173832758784

Offset: 0

N. J. A. Sloane

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 155, Table 6.6.1.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Sean A. Irvine, Table of n, a(n) for n = 0..50
F. Harary and E. M. Palmer, Enumeration of self-converse digraphs, Mathematika, 13 (1966), 151-157.

Equals A029849*2 - A000595. Cf. A002499.

In the Encyclopedia of Integer Sequences the n=6 term is given incorrectly as 484256.

Corrected and extended with formula by Christian G. Bower, Jun 15 1998

A054933 Number of unlabeled digraphs on n nodes up to reversing the arcs.

Original entry on oeis.org

1, 3, 13, 144, 5158, 778084, 441288796, 896699384640, 6513980949408584, 170630216624502796000, 16261454692830032538976880, 5683372715412978313604073582912, 7334542846356465411966209047539403296, 35157828307617499762304829312302735958971072, 629172630775224433640531447950565255471723325434560

Offset: 1

N. J. A. Sloane, May 24 2000

Andrew Howroyd, Table of n, a(n) for n = 1..50
A. Gainer-Dewar, Pólya theory for species with an equivariant group action, arXiv:1401.6202 [math.CO], 2014. Also Andrew Gainer-Dewar, Species with an equivariant group action, AUSTRALASIAN JOURNAL OF COMBINATORICS, Volume 63(2) (2015), Pages 202-225.
V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Cf. A000273, A002499.

A000273 = Cases[Import["https://oeis.org/A000273/b000273.txt", "Table"], {, }][[All, 2]];
A002499 = Cases[Import["https://oeis.org/A002499/b002499.txt", "Table"], {, }][[All, 2]];
a[n_] := (A000273[[n + 1]] + A002499[[n]])/2;
Array[a, 50] (* Jean-François Alcover, Aug 29 2019 *)

a(n) = (A000273(n) + A002499(n))/2.

A126067 Triangle read by rows: T(n,k) is the number of unlabeled self-converse digraphs with n nodes and k arcs, k=0..n*(n-1).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 3, 5, 9, 10, 12, 10, 9, 5, 3, 1, 1, 1, 1, 3, 6, 15, 24, 41, 57, 77, 84, 90, 84, 77, 57, 41, 24, 15, 6, 3, 1, 1, 1, 1, 3, 7, 20, 42, 91, 164, 295, 463, 683, 918, 1185, 1394, 1550, 1590, 1550, 1394, 1185, 918, 683, 463, 295, 164, 91, 42, 20, 7, 3, 1, 1

Offset: 0

Vladeta Jovovic, Feb 28 2007

			Triangle begins:
  1;
  1;
  1,1,1;
  1,1,2,2,2,1,1;
  1,1,3,5,9,10,12,10,9,5,3,1,1;
  1,1,3,6,15,24,41,57,77,84,90,84,77,57,41,24,15,6,3,1,1;
  ....

Andrew Howroyd, Table of n, a(n) for n = 0..2680 (rows 0..20)

Row sums are A002499.

Cf. A052283, A126066.

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(c=gcd(v[i], v[j])*if(v[i]*v[j]%2==0, 2, 1)); t(2*v[i]*v[j]/c)^c)) * prod(i=1, #v, my(c=v[i]); if(c%2, t(2*c)^(c\2), t(c)^(c-1-c%4/2)*t(c/2)^(c%4)))}
Row(n) = {my(s=0); forpart(p=n, s+=permcount(p)*edges(p, i->1+x^i)); Vecrev(s)/n!}
{ for(n=0, 5, print(Row(n))) } \\ Andrew Howroyd, Apr 19 2020

a(0)=1 prepended and terms a(46) and beyond from Andrew Howroyd, Apr 19 2020

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A047833 Erroneous version of A002499.

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A047834 Another erroneous version of A002499.

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A002500 Number of self-converse relations on n points.

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A054933 Number of unlabeled digraphs on n nodes up to reversing the arcs.

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A126067 Triangle read by rows: T(n,k) is the number of unlabeled self-converse digraphs with n nodes and k arcs, k=0..n*(n-1).

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