A361698 The number of unlabeled connected 4 regular multigraphs on n nodes with 4 external legs, loops allowed.

1, 1, 2, 8, 37, 181, 1010, 6135, 40893, 295753, 2317683, 19568427, 177397551, 1719790643, 17767328745, 194954224643, 2265042428226, 27785727158182, 358952560098959, 4871697965709175, 69309502018430799, 1031550920679805502, 16030923441853969843, 259682356008358417321, 4377679648827121988375

Offset

0,3

Comments

Alternatively, unlabeled connected multigraphs on n+4 nodes with 4 nodes of degree 1 and n nodes of degree 4.

Links

Table of n, a(n) for n=0..24.

H. Kleinert, A. Pelster, B. Kastening, and M. Bachmann, Recursive graphical construction of Feynman diagrams and their multiplicities in Phi^4 and Phi^2*A theory, Phys. Rev. E 62 (2) (2000), 1537 eq. (4.29)

Formula

G.f.: 1 + B(x)/(1 + C(x)) - (D(x)^2 + D(x^2))/2 where B(x), C(x) and D(x) are the g.f.s of A361454, A129429 and A361135, respectively. - Andrew Howroyd, Mar 21 2023

Crossrefs

Cf. A361135 (2 legs), A085549 (no legs), A129429, A361454 (not necessarily connected).

Sequence in context: A280119 A224032 A046814 * A305547 A007857 A289541

Adjacent sequences: A361695 A361696 A361697 * A361699 A361700 A361701

Keyword

nonn

Author

R. J. Mathar, Mar 21 2023

Extensions

Terms a(7) and beyond from Andrew Howroyd, Mar 21 2023

Status

approved