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Search: id:A100693
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| A100693 |
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Number of selfavoiding paths with n steps on a hexagonal lattice in the strip Z x {0,1,2}. |
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1
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| 1, 2, 3, 5, 6, 7, 9, 14, 14, 14, 22, 30, 28, 28, 44, 60, 56, 56, 88, 120, 112, 112, 176, 240, 224, 224, 352, 480, 448, 448, 704, 960, 896, 896, 1408, 1920, 1792, 1792, 2816, 3840, 3584, 3584, 5632, 7680, 7168, 7168, 11264, 15360, 14336, 14336, 22528, 30720
(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+2z+3z^2+5z^3+4z^4+3z^5+3z^6+4z^7+2z^8+4z^10+2z^11)/(1-2z^4). For n>=2: a(4n)=a(4n+1)=7*2^(n-1), a(4n+2)=11*2^(n-1), a(4n+3)=15*2^(n-1).
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MAPLE
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g:=series((1+2*z+3*z^2+5*z^3+4*z^4+3*z^5+3*z^6+4*z^7+2*z^8+4*z^10+2*z^11)/(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: A074780 A056900 A096594 this_sequence A030159 A030161 A129125
Adjacent sequences: A100690 A100691 A100692 this_sequence A100694 A100695 A100696
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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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