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%I #7 Mar 15 2018 04:39:02
%S 4,72,4176,731808,381879360,592267282560,2733202405059840,
%T 37590062966534453760,1542797317119230338360320,
%U 189160927199005707074274969600
%N This sequence with the appropriate denominator (product of (2*3^k-3) k=0..n) produces the expected length of shortest nonintersecting path through n points on a Sierpiński Gasket from corner to corner.
%C I am looking for the asymptotics of this sequence (scaled by the appropriate denominator). I'm convinced that a(n) / n^(1-log(2)/log(3)) -> constant but need to know more about sequence to solve this problem.
%p 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;
%K frac,nonn,uned
%O 0,1
%A Nathan B. Shank (nas2(AT)lehigh.edu), Nov 11 2002
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