A381123 Number of unlabeled endofunctions on n points whose self-referencing elements are mapped from another element.

1, 0, 2, 4, 12, 28, 83, 213, 608, 1664, 4703, 13173, 37412, 105995, 302301, 862794, 2470631, 7084425, 20357121, 58573788, 168789684, 486964114, 1406549550, 4066751083, 11769363663, 34090076148, 98820914068, 286672673725, 832183340955, 2417270306657, 7025657374736, 20430883575932, 59444386613999, 173039084438093

Offset

0,3

Comments

Equivalently, the number of digraphs on n unlabeled nodes where each node has an out degree 1 and, if it is self-referencing, it is referenced from at least one other node.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(0) = 1; a(n) = A001372(n) - A001372(n - 1) for n > 0.

Example

For n = 2 one node must reference the other one, this one may reference itself or the first one. So a(2) = 2.
For n = 3 there are 7 = A001372(3) endofunctions, but 3 = A001372(2) of them have at least 1 isolated element. So a(3) = 7 - 3 = 4.

Crossrefs

Partial differences of A001372.

Sequence in context: A275434 A364316 A383835 * A151258 A148175 A148176

Adjacent sequences: A381120 A381121 A381122 * A381124 A381125 A381126

Keyword

nonn

Author

Peter Dolland, Feb 14 2025

Status

approved