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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.
5
1, 1, 1, 2, 5, 18, 98, 779, 10589, 255790, 11633297, 1004417286, 163944008107, 50324877640599, 29001521193534445, 31396727025729968365, 63969154112074956299242, 245871360738448777028919520, 1787330701747389106609369225312, 24636017249593067184544456944967278
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Graph Bridge
Eric Weisstein's World of Mathematics, Endpoint
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
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