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A100691
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Number of self-avoiding paths with n steps on a triangular lattice in the strip Z x {0,1}.
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0
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1, 4, 12, 30, 70, 158, 352, 780, 1724, 3806, 8398, 18526, 40864, 90132, 198796, 438462, 967062, 2132926, 4704320, 10375708, 22884348, 50473022, 111321758, 245527870, 541528768, 1194379300, 2634286476, 5810101726, 12814582758
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OFFSET
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0,2
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REFERENCES
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J. Labelle, Paths in the Cartesian, triangular and hexagonal lattices, Bulletin of the ICA, 17, 1996, 47-61.
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LINKS
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FORMULA
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G.f.: (1+z^2)(1+z+z^2)/[(1-z)(1-2z-z^3)]= 1+2*(2+z^2)/((z-1)*(z^2+2*z-1)).
a(n) = 2*a(n-1) + a(n-3) + 6 for n >= 4.
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MAPLE
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g:=series((1+z^2)*(1+z+z^2)/(1-z)/(1-2*z-z^3), z=0, 35): 1, seq(coeff(g, z^n), n=1..34);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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