cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A005642 Number of 2-diregular connected digraphs with n nodes.

Original entry on oeis.org

1, 3, 7, 24, 117, 663, 4824, 40367, 381554, 4001849, 46043780, 576018785, 7783281188, 112953364381, 1752128923245, 28930230194371, 506596534953769
Offset: 2

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Author

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A005641 (not necess. connected), A306892 (multiarcs allowed). Labeled version is A123544.

A006372 Numbers of terms in expressions for coefficients of "Lovelock Lagrangians" (or "Gauss-Bonnet forms") in terms of Riemann-Christoffel curvature tensor and two of its contractions (viz., the Ricci curvature tensor and the Riemann curvature scalar) for n-dimensional differentiable manifolds having a general linear connection.

Original entry on oeis.org

1, 1, 3, 8, 25, 85, 397, 2183, 15129, 122585
Offset: 0

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Author

C. C. Briggs (ccb104(AT)vm.cac.psu.edu)

Keywords

Crossrefs

Cf. A006373, A045900 (conjectural), A306892 (2-regular digraphs).

Extensions

a(6)-a(8) from R. J. Mathar, Apr 08 2019
a(9) added by R. J. Mathar, Apr 15 2019

A306827 Isomorphism classes of connected 2-in 2-out digraphs, allowing parallel edges but not loops.

Original entry on oeis.org

1, 2, 5, 13, 59, 285, 1987, 16057, 149430, 1551863, 17747299, 221015026
Offset: 2

Views

Author

Brendan McKay, Mar 12 2019

Keywords

Comments

From R. J. Mathar, Mar 15 2019: (Start)
The multiset transform (graphs with n>=2 nodes and k>=1 components) is
1
2
5 1
13 2
59 8 1
285 23 2
1987 100 8 1
16057 468 27 2
149430 2943 115 8 1
The row sums (Euler transform) are A307180. (End)

Examples

			For n=3, the a(3)=2 solutions consist of two superimposed directed triangles, one with the triangles oriented consistently and the other with the triangles oriented oppositely.
		

Crossrefs

Cf. A219889 (no multiedges, not necessarily connected), A306892 (loops permitted), A307180 (Euler transf.)
Showing 1-3 of 3 results.