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A116950 Number of functional patterns on n elements; or digraphs with maximum outdegree 1, n arrows and every point connected to an arrow. 4
1, 2, 7, 20, 61, 174, 514, 1478, 4303, 12437, 36084, 104494, 303167, 879283, 2552803, 7413583, 21544347, 62635823, 182199853, 530228946, 1543761513, 4496523995, 13102414665, 38193626823, 111375529695, 324891970936, 948051861938, 2767336312386, 8080206646244 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A001372 counts functional patterns from a set with n elements to itself; A000041 (partition function) counts functional patterns from a set with n elements to a disjoint set; this is the general case where the range may overlap the domain but may also include other values.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2127

FORMULA

Euler transform of A002861(n) + A000081(n+1).

a(n) ~ c * d^n / sqrt(n), where d = A051491 = 2.95576528565199497471481752412..., c = 3.435908969217935496995961718... . - Vaclav Kotesovec, Sep 10 2014

EXAMPLE

For n=2 there are the following 7 digraphs:

o-+.o-+ o->o-+ o->o o-+.o->o o->o->o o->o o->o

^.|.^.| ...^.| ^..| ^.|..... ....... ...^ ....

+-+.+-+ ...+-+ +--+ +-+..... ....... o--+ o->o

MATHEMATICA

nmax = 750;

A002861 = Cases[Import["https://oeis.org/A002861/b002861.txt", "Table"], {_, _}][[;; nmax + 2, 2]];

A000081 = Cases[Import["https://oeis.org/A000081/b000081.txt", "Table"], {_, _}][[;; nmax + 2, 2]];

etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n - j], {j, 1, n}]/n]; b];

b[n_] := A002861[[n]] + A000081[[n + 2]];

a = etr[b];

a[0] = 1;

a /@ Range[0, nmax](* Jean-Fran├žois Alcover, Mar 13 2020 *)

CROSSREFS

Cf. A000041, A001372, A002861, A000081.

Sequence in context: A026153 A025180 A201967 * A111017 A116408 A015518

Adjacent sequences:  A116947 A116948 A116949 * A116951 A116952 A116953

KEYWORD

easy,nice,nonn

AUTHOR

Franklin T. Adams-Watters, Mar 29 2006

STATUS

approved

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Last modified April 22 10:24 EDT 2021. Contains 343174 sequences. (Running on oeis4.)