A076744 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.

4, 72, 4176, 731808, 381879360, 592267282560, 2733202405059840, 37590062966534453760, 1542797317119230338360320, 189160927199005707074274969600

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^(1-log(2)/log(3)) -> constant but need to know more about sequence to solve this problem.

Links

Table of n, a(n) for n=0..9.

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

Sequence in context: A013102 A224900 A012995 * A177392 A158269 A024257

Adjacent sequences: A076741 A076742 A076743 * A076745 A076746 A076747

Keyword

frac,nonn,uned

Author

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

Status

approved