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Search: id:A116950
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| A116950 |
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Number of functional patterns on n elements; or digraphs with maximum outdegree 1, n arrows, and every point connected to an arrow. |
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+0
4
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| 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
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FORMULA
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Euler transform of A002861(n) + A000081(n+1).
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EXAMPLE
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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
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CROSSREFS
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Cf. A000041, A001372, A002861, A000081.
Sequence in context: A026124 A026153 A025180 this_sequence A111017 A116408 A014983
Adjacent sequences: A116947 A116948 A116949 this_sequence A116951 A116952 A116953
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 29 2006
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