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<DIV>Hi,<BR>I subscribed to Jussieu Campus Computing Center mailing list and
received your kind response reading:</DIV>
<DIV> </DIV>
<DIV>Quote<Welcome, Bienvenue to this mailing list hosted by the List
Server<BR>of Jussieu Campus Computing Center, Paris, France. [...]<BR>The
requirement for subscribers is to have already contributed at least<BR>five
different (and interesting) integer sequences to the Online EIS
Database>unquote</DIV>
<DIV> </DIV>
<DIV>From this I cannot make up whether or not I am subscribed. Am
I?<BR>I entered one sequence that I reproduce below. I don't think it is in the
data base for I can't find it.</DIV>
<DIV>What will happen now?</DIV>
<DIV>Best wishes, Jos Koot</DIV>
<DIV> </DIV>
<DIV>#| This one I already entered in the database.<BR>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:</DIV>
<DIV>N(1) = 2<BR>N(n+1) = N(n)^2 + N(n)^3</DIV>
<DIV>By adopting N(0)=1 we may define:<BR>N(0) = 1<BR>N(n+1) = N(n)^2 +
N(n)^3<BR>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.</DIV>
<DIV>It's a fast groing series. logN(n) grows somewhat faster than O(3^n)</DIV>
<DIV>Scheme|#</DIV>
<DIV> </DIV>
<DIV>(define (next n) (* n n (+ n 1)))</DIV>
<DIV> </DIV>
<DIV>(define (list-elements nr-of-elements n0 next)<BR> (let list-elements
((i 0) (n n0))<BR> (show i n)<BR> (let ((i (add1
i)))<BR> (if (< i nr-of-elements) (list-elements i (next
n))))))</DIV>
<DIV> </DIV>
<DIV>(define (show i n) (printf "N(~a)=~a~n~n" i n))</DIV>
<DIV> </DIV>
<DIV>(list-elements 6 1 next)</DIV>
<DIV> </DIV>
<DIV>#|<BR>N(0)=1</DIV>
<DIV> </DIV>
<DIV>N(1)=2</DIV>
<DIV> </DIV>
<DIV>N(2)=12</DIV>
<DIV> </DIV>
<DIV>N(3)=1872</DIV>
<DIV> </DIV>
<DIV>N(4)=6563711232</DIV>
<DIV> </DIV>
<DIV>N(5)=282779810171805015122254036992</DIV>
<DIV> </DIV>
<DIV>N(6)=226123238024163027405724665329~</DIV>
<DIV>05158028496454353087246911545156210~</DIV>
<DIV>129751385945830223511552</DIV>
<DIV> </DIV>
<DIV>N(7)=11562069815038130018873694782045080~</DIV>
<DIV>7119408025468383191778410018183203255400~</DIV>
<DIV>3505982560975883138497594952511247662249~</DIV>
<DIV>1299802627898583353363769509453976699991~</DIV>
<DIV>0069017660827182318971612750901196669134~</DIV>
<DIV>5154362281773776744778952384776931291833~</DIV>
<DIV>4512355701653105181591508877312|#</DIV></BODY></HTML>