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A100691
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Number of selfavoiding 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| J. Labelle, Paths in the cartesian, triangular and hexagonal lattices, Bulletin of the ICA, 17, 1996, 47-61.
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FORMULA
| G.f=(1+z^2)(1+z+z^2)/[(1-z)(1-2z-z^3)]. a(n)=2a(n-1)+a(n-3)+6 for n>=4.
a(n) = A008998(n+2) - A052980(n+1) - 3. - Ralf Stephan, May 15 2007
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MAPLE
| 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
| Sequence in context: A036388 A037166 A118892 * A000298 A006802 A068055
Adjacent sequences: A100688 A100689 A100690 * A100692 A100693 A100694
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 07 2004
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