A004115 Number of unlabeled rooted nonseparable graphs with n nodes. (Formerly M3592)

0, 1, 1, 4, 22, 178, 2278, 46380, 1578060, 92765486, 9676866173, 1821391854302, 625710416245358, 395761853562201960, 464128290507379386872, 1015085639712281997464676, 4160440039279630394986003604, 32088534920274236421098827156776

Offset

1,4

References

R. W. Robinson, personal communication.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

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

Links

Andrew Howroyd, Table of n, a(n) for n = 1..40 (terms 1..26 from R. W. Robinson)

R. W. Robinson, Rooted non-separable graphs - computer printout

Prog

(PARI) \\ See links in A339645 for combinatorial species functions.
edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}
graphsCycleIndex(n)={my(s=0); forpart(p=n, s+=permcount(p) * 2^edges(p) * sMonomial(p)); s/n!}
graphsSeries(n)={sum(k=0, n, graphsCycleIndex(k)*x^k) + O(x*x^n)}
cycleIndexSeries(n)={my(g=graphsSeries(n), gcr=sPoint(g)/g); x*sSolve( sLog( gcr/(x*sv(1)) ), gcr )}
{ my(N=15); Vec(OgfSeries(cycleIndexSeries(N)), -N) } \\ Andrew Howroyd, Dec 25 2020

Crossrefs

Cf. A002218, A007145, A013922.

Sequence in context: A294343 A259842 A125863 * A362747 A222885 A235329

Adjacent sequences: A004112 A004113 A004114 * A004116 A004117 A004118

Keyword

nonn,nice

Author

N. J. A. Sloane

Status

approved