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A307205
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Coordination sequence for tetravalent node in the first Moore pentagonal tiling.
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7
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1, 4, 8, 14, 19, 24, 29, 36, 44, 48, 54, 58, 69, 68, 77, 80, 94, 88, 100, 102, 119, 108, 123, 124, 144, 128, 146, 146, 169, 148, 169, 168, 194, 168, 192, 190, 219, 188, 215, 212, 244, 208, 238, 234, 269, 228, 261, 256, 294, 248, 284, 278, 319, 268, 307, 300
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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 >= 7, a(n+4) = a(n) + [25,20,23,22] according as n == [0,1,2,3] mod 4. - Chaim Goodman-Strauss, Mar 31 2019
G.f.: (1 + 4*x + 8*x^2 + 14*x^3 + 17*x^4 + 16*x^5 + 13*x^6 + 8*x^7 + 7*x^8 + 4*x^9 + 4*x^10 - 4*x^13 - 2*x^14) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
a(n) = 2*a(n-4) - a(n-8) for n>14.
(End)
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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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