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A322700 Number of unlabeled graphs with loops spanning n vertices. 1
1, 1, 4, 14, 70, 454, 4552, 74168, 2129348, 111535148, 10812483376, 1945437208224, 650378721156736, 404749938336404704, 470163239887698967104, 1022592854829028311090816, 4177826139658552046627175072, 32163829440870460348768023969632 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The span of a graph is the union of its edges. The not necessarily spanning case is A000666.

LINKS

Table of n, a(n) for n=0..17.

Gus Wiseman, Non-isomorphic representatives of the a(4) = 70 spanning graphs with loops.

FORMULA

First differences of A000666.

MATHEMATICA

Table[Sum[2^PermutationCycles[Ordering[Map[Sort, Select[Tuples[Range[n], 2], OrderedQ]/.Rule@@@Table[{i, prm[[i]]}, {i, n}], {1}]], Length], {prm, Permutations[Range[n]]}]/n!, {n, 0, 8}]//Differences (* Mathematica 8.0+ *)

CROSSREFS

Cf. A000666, A006125, A006129, A054921, A062740, A320461, A322635, A322661.

Sequence in context: A050549 A222980 A321273 * A167144 A159483 A088127

Adjacent sequences:  A322697 A322698 A322699 * A322701 A322702 A322703

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 23 2018

STATUS

approved

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Last modified January 24 10:52 EST 2020. Contains 331193 sequences. (Running on oeis4.)