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Search: id:A100692
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| A100692 |
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Number of selfavoiding paths with n steps on a hexagonal lattice in the strip Z x {-1,0,1}. |
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+0
1
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| 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; listen)
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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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FORMULA
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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
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MAPLE
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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);
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CROSSREFS
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Sequence in context: A112376 A078490 A047877 this_sequence A089640 A086659 A008473
Adjacent sequences: A100689 A100690 A100691 this_sequence A100693 A100694 A100695
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 07 2004
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