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 A100692 Number of selfavoiding paths with n steps on a hexagonal lattice in the strip Z x {-1,0,1}. 0
 1, 3, 4, 4, 6, 10, 10, 8, 12, 20, 20, 16, 24, 40, 40, 32, 48, 80, 80, 64, 96, 160, 160, 128, 192, 320, 320, 256, 384, 640, 640, 512, 768, 1280, 1280, 1024, 1536, 2560, 2560, 2048, 3072, 5120, 5120, 4096, 6144, 10240, 10240, 8192, 12288, 20480, 20480, 16384 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES J. Labelle, Paths in the cartesian, triangular and hexagonal lattices, Bulletin of the ICA, 17, 1996, 47-61. LINKS FORMULA G.f.=(1+3z+4z^2+4z^3+4z^4+4z^5+2z^6)/(1-2z^4). a(0)=1, a(1)=3, a(2)=4, a(4n+3)=4*2^n, a(4n+4)=6*2^n, a(4n+5)=a(4n+6)=10*2^n. - Ralf Stephan, May 16 2007 MAPLE g:=series((1+3*z+4*z^2+4*z^3+4*z^4+4*z^5+2*z^6)/(1-2*z^4), z=0, 64): 1, seq(coeff(g, z^n), n=1..60); CROSSREFS Sequence in context: A224212 A078490 A047877 * A089640 A086659 A008473 Adjacent sequences:  A100689 A100690 A100691 * A100693 A100694 A100695 KEYWORD nonn AUTHOR Emeric Deutsch, Dec 07 2004 STATUS approved

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