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%I M3450 #28 May 12 2023 15:56:56
%S 1,4,12,36,108,316,916,2628,7500,21268,60092,169092,474924,1329188,
%T 3715244,10359636,28856252,80220244,222847804,618083972,1713283628,
%U 4742946484,13123882524,36274940740,100226653420,276669062116,763482430316,2105208491748,5803285527724
%N Trails of length n on square lattice.
%C A trail is a path which may cross itself but does not reuse an edge. This sequence counts directed paths on the square lattice.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrey Zabolotskiy, <a href="/A006817/b006817.txt">Table of n, a(n) for n = 0..31</a> (from Conway & Guttmann; terms 0..30 from Bert Dobbelaere)
%H A. R. Conway and A. J. Guttmann, <a href="https://doi.org/10.1088/0305-4470/26/7/013">Enumeration of self-avoiding trails on a square lattice using a transfer matrix technique</a>, J. Phys. A: Math. Gen., 26 (1993), 1535-1552; arXiv:<a href="https://arxiv.org/abs/hep-lat/9211063">hep-lat/9211063</a>, 1992.
%H A. J. Guttmann, <a href="https://doi.org/10.1088/0305-4470/18/4/009">Lattice trails II: numerical results</a>, J. Phys. A 22 (1989), 575-588.
%H A. Malakis, <a href="https://doi.org/10.1088/0305-4470/9/8/018">The trail problem on the square lattice</a>, J. Phys A 9 (8) (1976) p 1283. Table 1.
%Y Undirected trails-rotation and reflection are counted by A001997.
%Y Cf. A006818, A006819, A006851.
%K nonn,walk
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_, Jul 20 2001
%E More terms from _Bert Dobbelaere_, Jan 19 2019