A189771 Number of simple graphs on n nodes that are Euler (all nodes even) but not Eulerian (single cycle passes through all edges).

0, 0, 0, 0, 0, 1, 2, 7, 20, 76, 334, 2498, 36398, 1225629, 89060804, 12978995815, 3646305137905, 1947685504386516, 1969840087225045340, 3770491704215436784514, 13674048211165798257589446, 94122727377410134768239226418

Offset

1,7

Comments

There are more Euler graphs than Eulerian graphs since there exist disconnected graphs having multiple disjoint cycles with each node even but for which no single cycle passes through all edges.

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Euler Graph

Eric Weisstein's World of Mathematics, Eulerian Graph

Formula

a(n) = A002854(n) - A133736(n).

Crossrefs

Cf. A002854, A133736.

Sequence in context: A095268 A118397 A171191 * A260504 A009697 A139012

Adjacent sequences: A189768 A189769 A189770 * A189772 A189773 A189774

Keyword

nonn

Author

Eric W. Weisstein, Apr 26 2011

Status

approved