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%I M5303 #31 May 20 2022 04:40:28
%S 1,52,358,1304,3455,7556,14532,25488,41709,64660,95986,137512,191243,
%T 259364,344240,448416,574617,725748,904894,1115320,1360471,1643972,
%U 1969628,2341424,2763525,3240276,3776202,4376008,5044579,5786980,6608456,7514432,8510513,9602484
%N Number of n-step mappings with 5 inputs.
%C Hogg & Huberman paper has a misprint a(4)=304. - _Sean A. Irvine_, Oct 11 2016
%D T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A005946/b005946.txt">Table of n, a(n) for n = 1..10000</a>
%H T. Hogg and B. A. Huberman, <a href="/A000258/a000258.pdf">Attractors on finite sets: the dissipative dynamics of computing structures</a>, Phys. Review A 32 (1985), 2338-2346. (Annotated scanned copy)
%H B. A. Huberman, T. H. Hogg, & N. J. A. Sloane, <a href="/A005945/a005945.pdf">Correspondence, 1985</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = h(5,n) where h(n, m) = Sum_{j} (n!/f(j)) * Product_{k=1..n} h(k,m-1)^(j(k)) and the sum runs over all partitions j=(j(1),...,j(n)) of n and f(j) = Product_{k=1..n} j(k)! * (k!)^(j(k)). That is, j satisfies Sum_{k=1..n} k*j(k) = n [From Hogg & Huberman]. - _Sean A. Irvine_, Oct 11 2016
%F G.f.: x*(24*x^3+108*x^2+47*x+1)/(1-x)^5. - _Alois P. Heinz_, Aug 23 2021
%p b:= proc(n, k) option remember; `if`(k=0, `if`(n<2, 1, 0),
%p add(Stirling2(n, j)*b(j, k-1), j=0..n))
%p end:
%p a:= n-> b(5, n):
%p seq(a(n), n=1..36); # _Alois P. Heinz_, Aug 23 2021
%t LinearRecurrence[{5, -10, 10, -5, 1}, {1, 52, 358, 1304, 3455}, 36] (* _Jean-François Alcover_, May 20 2022 *)
%Y Row n=5 of A144150.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_.
%E a(4) corrected and more terms from _Sean A. Irvine_, Oct 11 2016
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