A005946 Number of n-step mappings with 5 inputs. (Formerly M5303)

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

1,2

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).

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

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 *)

Crossrefs

Row n=5 of A144150.

Sequence in context: A264494 A232404 A257940 * A200549 A000527 A294055

Adjacent sequences: A005943 A005944 A005945 * A005947 A005948 A005949

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

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

Status

approved