Riffs & Rotes

Jon Awbrey jawbrey at att.net
Mon Jul 4 02:08:05 CEST 2005


R&R.  Note 23



Here's a combinatorial interpretation of a rapidly growing sequence in the OEIS:

%I A050924
%S A050924 1,2,9,1000000000
%N A050924 a(n) = (a(n-1)+1)^(a(n-1)), a(1) = 1.
%C A050924 Let S(1) c S(2) c ... c S(n) c ... be an increasing sequence of sets of
           partial functions that is defined as follows:  S(1) = {empty function},
           S(n) = {partial functions: S(n-1) -> S(n-1)}.  Then |S(n)| = a(n). - 
           Jon Awbrey (jawbrey(AT)att.net), Jul 04 2005
%Y A050924 Cf. A109300, A109301.
%Y A050924 Sequence in context: A030252 A049384 A103562
           this_sequence A096877 A058297 A100078
%Y A050924 Adjacent sequences: A050921 A050922 A050923
           this_sequence A050925 A050926 A050927
%K A050924 easy,nonn
%O A050924 1,2
%A A050924 Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 30 1999

This is so because the number of partial functions from
a finite domain D to a finite codomain C is (|C|+1)^|D|.

Jon Awbrey

inquiry e-lab: http://stderr.org/pipermail/inquiry/

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