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A307202
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Coordination sequence for trivalent node of type alpha' in the first Moore pentagonal tiling.
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7
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1, 3, 9, 15, 21, 24, 30, 42, 42, 45, 51, 69, 63, 66, 72, 96, 84, 87, 93, 123, 105, 108, 114, 150, 126, 129, 135, 177, 147, 150, 156, 204, 168, 171, 177, 231, 189, 192, 198, 258, 210, 213, 219, 285, 231, 234, 240, 312, 252, 255, 261, 339, 273, 276, 282, 366
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OFFSET
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0,2
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COMMENTS
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There are six orbits on nodes, and six distinct coordination sequences, which are A307201 (nodes of type alpha), A307202 (alpha'), A307203 (alpha''), A307270 (alpha'''), A307204 (alpha''''), and A307206 (beta).
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REFERENCES
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Herbert C. Moore, U.S. Patent 928,320, Patented July 20 1909.
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LINKS
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FORMULA
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For n >= 1, a(n+4) = a(n) + [21,21,21,27] according as n == [0,1,2,3] mod 4. - Chaim Goodman-Strauss, Mar 31 2019
G.f.: (1 + 3*x + 9*x^2 + 15*x^3 + 19*x^4 + 18*x^5 + 12*x^6 + 12*x^7 + x^8) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
a(n) = 2*a(n-4) - a(n-8) for n>8. (End)
E.g.f.: (4 - 3*(x - 1)*cos(x) + 3*(8*x - 1)*cosh(x) + 6*sin(x) + 3*(7*x - 5)*sinh(x))/4. Stefano Spezia, Sep 07 2022
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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