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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(4) corrected and more terms from Sean A. Irvine, Oct 11 2016
STATUS
approved