A322396 Number of unlabeled simple connected graphs with n vertices whose bridges are all leaves, meaning at least one end of any bridge is an endpoint of the graph.

1, 1, 1, 2, 5, 18, 98, 779, 10589, 255790, 11633297, 1004417286, 163944008107, 50324877640599, 29001521193534445, 31396727025729968365, 63969154112074956299242, 245871360738448777028919520, 1787330701747389106609369225312, 24636017249593067184544456944967278

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..25

Eric Weisstein's World of Mathematics, Graph Bridge

Eric Weisstein's World of Mathematics, Endpoint

Gus Wiseman, The a(5) = 18 simple connected graphs whose bridges are all leaves.

Prog

(PARI) \\ See A004115 for graphsSeries and A339645 for combinatorial species functions.
bridgelessGraphs(n)={my(gc=sLog(graphsSeries(n)), gcr=sPoint(gc)); sSolve( gc + gcr^2/2 - sRaise(gcr, 2)/2, x*sv(1)*sExp(gcr) )}
cycleIndexSeries(n)={1+sSubstOp(bridgelessGraphs(n), symGroupSeries(n))}
NumUnlabeledObjsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Dec 31 2020

Crossrefs

Cf. A001187, A006125, A007146, A013922, A054921, A095983, A322338, A322394, A322395.

Sequence in context: A187008 A333837 A075634 * A007127 A279207 A005639

Adjacent sequences: A322393 A322394 A322395 * A322397 A322398 A322399

Keyword

nonn

Author

Gus Wiseman, Dec 06 2018

Extensions

a(6)-a(10) from Andrew Howroyd, Dec 08 2018

Terms a(11) and beyond from Andrew Howroyd, Dec 31 2020

Status

approved