

A076744


This sequence with the appropriate denominator (product of (2*3^k3) k=0..n) produces the expected length of shortest nonintersecting path through n points on a Sierpiński Gasket from corner to corner.


0




OFFSET

0,1


COMMENTS

I am looking for the asymptotics of this sequence (scaled by the appropriate denominator). I'm convinced that a(n) / n^(1log(2)/log(3)) > constant but need to know more about sequence to solve this problem.


LINKS



MAPLE

with(combinat, numbcomb): ntop := 25: for n from 1 to ntop do a[n] := sum('numbcomb(n, k)*(1)^k*1/(2*3^k  3)', 'k'=0..n): b[n] := product('2*3^k  3', 'k'=0..n): od: for n from 1 to ntop do c[n] := solve(x/b[n] = a[n]); od;


CROSSREFS



KEYWORD

frac,nonn,uned


AUTHOR

Nathan B. Shank (nas2(AT)lehigh.edu), Nov 11 2002


STATUS

approved



