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

Author

Jonathan Vos Post, Feb 06 2007

Keywords

• easy
• nonn

Comments

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

Examples

			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.
		

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

• Eric Weisstein's World of Mathematics, Functional Graph.

Crossrefs

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

Formula

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

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