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A006815 Related to self-avoiding walks on square lattice.
(Formerly M4157)

%I M4157 #15 Aug 09 2017 21:47:28

%S 1,6,23,84,283,930,2921,9096,27507,82930,244819,722116,2096603,

%T 6087290,17458887,50090544,142317089,404543142

%N Related to self-avoiding walks on square lattice.

%C After constructing a self-avoiding walk, bridge together all adjacent neighboring sites on the walk. a(n) is the sum of the lengths of the shortest path in each of the resulting structures from beginning to end (i.e., using the original path and any bridges), across all walks of length n. My attempt to compute this sequence diverges from the listed terms at n=9, for which I get a(9)=27511, a(10)=82938, .... - _Sean A. Irvine_, Aug 09 2017

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H S. S. Manna, A. J. Guttmann and A. K. Roy, <a href="https://doi.org/10.1088/0305-4470/22/17/026">Diffusion on self-avoiding walk networks</a>, J. Phys. A 22 (1989), 3621-3627.

%Y Cf. A006814, A006816.

%K nonn,walk,more

%O 1,2

%A _N. J. A. Sloane_

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Last modified March 1 20:05 EST 2024. Contains 370443 sequences. (Running on oeis4.)