login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005946 Number of n-step mappings with 5 inputs.
(Formerly M5303)
2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 10 16:20 EDT 2022. Contains 356039 sequences. (Running on oeis4.)