A263105 Number of distinct cycles without repeated edges in the multigraph on 3 vertices, with n edges between each pair of vertices.

1, 33, 2916, 808300, 509131545, 605707523361, 1214620662420928, 3795417851074101456, 17444500147778706611145, 112823815631393432721650905, 991377088026896964421518306036, 11502248569873461404933124399742188

Offset

1,2

Comments

Cycles have length at least 2, and may repeat vertices but not edges.

Cycles p,q are equivalent if the vertex-edge sequence of q can be made by rotating or reversing that of p.

Links

Simon R. Donnelly, Table of n, a(n) for n = 1..60

Simon R. Donnelly, Python program

Eric W. Weisstein, Multigraph

Example

For n=2 the a(n) = 33 unique cycles' vertex-edge sequences are:
a0b1a, b2c3b, c4a5c;
a0b2c4a, a0b2c5a, a0b3c4a, a0b3c5a, a1b2c4a, a1b2c5a, a1b3c4a, a1b3c5a;
a0b2c3b1a, a0b3c2b1a, b2c4a5c3b, b2c5a4c3b, c4a0b1a5c, c4a1b0a5c;
a0b2c4a1b3c5a, a1b2c4a0b3c5a, a0b3c4a1b2c5a, a0b2c5a1b3c4a;
a0b2c4a5c3b1a, a1b2c4a5c3b0a, a0b3c4a5c2b1a, a0b2c5a4c3b1a;
b2c4a0b1a5c3b, b3c4a0b1a5c2b, b2c5a0b1a4c3b, b2c4a1b0a5c3b;
c4a0b3c4b1a5c, c5a0b3c4b1a4c, c4a1b3c4b0a5c, c4a0b4c3b1a5c.

Prog

(Python) # See links.

Crossrefs

Sequence in context: A358808 A111922 A136541 * A284072 A281444 A242019

Adjacent sequences: A263102 A263103 A263104 * A263106 A263107 A263108

Keyword

nonn,walk

Author

Simon R. Donnelly, Oct 09 2015

Status

approved