A005946 Number of n-step mappings with 5 inputs.

1, 52, 358, 1304, 3455, 7556, 14532, 25488, 41709, 64660, 95986, 137512, 191243, 259364, 344240, 448416, 574617, 725748, 904894, 1115320, 1360471, 1643972, 1969628, 2341424, 2763525, 3240276, 3776202, 4376008, 5044579, 5786980, 6608456, 7514432, 8510513, 9602484

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Hogg & Huberman paper has a misprint a(4)=304. - Sean A. Irvine, Oct 11 2016

References

• T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346. (Annotated scanned copy)
• B. A. Huberman, T. H. Hogg, & N. J. A. Sloane, Correspondence, 1985
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Row n=5 of A144150.

Programs

Maple

b:= proc(n, k) option remember; `if`(k=0, `if`(n<2, 1, 0),
      add(Stirling2(n, j)*b(j, k-1), j=0..n))
    end:
a:= n-> b(5, n):
seq(a(n), n=1..36);  # Alois P. Heinz, Aug 23 2021

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {1, 52, 358, 1304, 3455}, 36] (* Jean-François Alcover, May 20 2022 *)

Formula

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

G.f.: x*(24*x^3+108*x^2+47*x+1)/(1-x)^5. - Alois P. Heinz, Aug 23 2021

Extensions

a(4) corrected and more terms from Sean A. Irvine, Oct 11 2016