my subscription

[jos koot]

Hi,
I subscribed to Jussieu Campus Computing Center mailing list and received your kind response reading:

Quote<Welcome, Bienvenue to this mailing list hosted by the List Server
of Jussieu Campus Computing Center, Paris, France.  [...]
The requirement for subscribers is to have already contributed at least
five different (and interesting) integer sequences to the Online EIS Database>unquote

 From this I cannot make up whether or not I am subscribed. Am I?
I entered one sequence that I reproduce below. I don't think it is in the data base for I can't find it.
What will happen now?
Best wishes, Jos Koot

#| This one I already entered in the database.
Let N(h) be the number of non self crossing ways of moving a Tower of Hanoi of h disks from one peg onto another peg, i.e. a sequence of moves starting with all disks on the starting peg, ending with all disks on the destination peg and never more than once producing the same distribution of disks among the pegs (assuming 3 pegs) We have:
N(1) = 2
N(n+1) = N(n)^2 + N(n)^3
By adopting N(0)=1 we may define:
N(0) = 1
N(n+1) = N(n)^2 + N(n)^3
I don't now a formula that expresses N(n) in n without recursion and I am (not yet) familiar enough with generating functions to find it myself.
It's a fast groing series. logN(n) grows somewhat faster than O(3^n)
Scheme|#

(define (next n) (* n n (+ n 1)))

(define (list-elements nr-of-elements n0 next)
 (let list-elements ((i 0) (n n0))
  (show i n)
  (let ((i (add1 i)))
   (if (< i nr-of-elements) (list-elements i (next n))))))

(define (show i n) (printf "N(~a)=~a~n~n" i n))

(list-elements 6 1 next)

#|
N(0)=1

N(1)=2

N(2)=12

N(3)=1872

N(4)=6563711232

N(5)=282779810171805015122254036992

N(6)=226123238024163027405724665329~
05158028496454353087246911545156210~
129751385945830223511552

N(7)=11562069815038130018873694782045080~
7119408025468383191778410018183203255400~
3505982560975883138497594952511247662249~
1299802627898583353363769509453976699991~
0069017660827182318971612750901196669134~
5154362281773776744778952384776931291833~
4512355701653105181591508877312|#
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