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A038579
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Number of self-avoiding closed walks from 0 of area n in strip Z X {0,1,2}.
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0
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1, 4, 10, 28, 64, 140, 304, 640, 1326, 2716, 5502, 11052, 22044, 43700, 86180, 169184, 330810, 644564, 1251954, 2424860, 4684696, 9029756, 17368408, 33343520, 63899686, 122259372, 233568998, 445600236, 849014964, 1615709156, 3071307852
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OFFSET
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0,2
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REFERENCES
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J. Labelle, Self-avoiding walks and polyominoes in strips, Bull. ICA, 23 (1998), 88-98.
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LINKS
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FORMULA
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G.f.: 2(1+2x^3+2x^4)/(1-x-x^2-x^3)^2-1 [Labelle]. - Emeric Deutsch, Apr 29 2004
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MATHEMATICA
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CoefficientList[ Series[(2 + 4 x^3 + 4 x^4)/(1 - x - x^2 - x^3)^2 - 1, {x, 0, 28}], x]
LinearRecurrence[{2, 1, 0, -3, -2, -1}, {1, 4, 10, 28, 64, 140, 304}, 31] (* Robert P. P. McKone, Jan 28 2021, same method used in A038578 MMA *)
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PROG
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(PARI) Vec(2*(1+2*x^3+2*x^4)/(1-x-x^2-x^3)^2-1+ O(x^40)) \\ Michel Marcus, Jan 28 2021
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CROSSREFS
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KEYWORD
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nonn,walk,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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