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 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. 0
 4, 72, 4176, 731808, 381879360, 592267282560, 2733202405059840, 37590062966534453760, 1542797317119230338360320, 189160927199005707074274969600 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 19 17:03 EDT 2024. Contains 374410 sequences. (Running on oeis4.)