A127911 Number of nonisomorphic partial functional graphs with n points which are not functional graphs.

0, 1, 3, 9, 26, 74, 208, 586, 1647, 4646, 13135, 37247, 105896, 301880, 862498, 2469480, 7083690, 20353886, 58571805, 168780848, 486958481, 1406524978, 4066735979, 11769294050, 34090034328, 98820719105, 286672555274

Offset

0,3

Comments

Partial functional graphs (digraphs) with at least one node of outdegree = 0.

References

S. Skiena, "Functional Graphs." Section 4.5.2 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 164-165, 1990.

Links

Table of n, a(n) for n=0..26.

Eric Weisstein's World of Mathematics, Functional Graph.

Formula

a(n) = A126285(n) - A001372(n).

Euler transform of (A002861 + A000081) - Euler transform of A002861.

Example

a(0) = 0 because the null graph is trivially both partial functional and functional.
a(1) = 1 because there are two partial functional graphs on one point: the point with, or without, a loop; the point with loop is the identity function, but without a loop the naked point is the unique merely partial functional case.
a(2) = 3 because there are A126285(2) enumerates the 6 partial functional graphs on 2 points, of which 3 are functional, 6 - 3 = 3.
a(3) = A126285(3) - A001372(3) = 16 - 7 = 9.
a(4) = 45 - 19 = 26.
a(5) = 121 - 47 = 74.
a(6) = 338 - 130 = 208.
a(7) = 929 - 343 = 586.
a(8) = 2598 - 951 = 1647.
a(9) = 7261 - 2615 = 4646.
a(10) = 20453 - 7318 = 13135.

Crossrefs

Cf. A000081, A000273, A001372, A002861, A003027, A003085, A062738, A116950, A126285, A127909-A127915.

Sequence in context: A234270 A258911 A268093 * A116423 A077845 A291000

Adjacent sequences: A127908 A127909 A127910 * A127912 A127913 A127914

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 06 2007

Status

approved