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A307204
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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, 6, 6, 12, 18, 24, 30, 30, 33, 48, 57, 60, 60, 72, 84, 78, 81, 96, 111, 96, 102, 120, 138, 114, 123, 144, 165, 132, 144, 168, 192, 150, 165, 192, 219, 168, 186, 216, 246, 186, 207, 240, 273, 204, 228, 264, 300, 222, 249, 288, 327, 240, 270, 312, 354, 258
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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 >= 10, a(n+4) = a(n) + [18,21,24,27] according as n == [0,1,2,3] mod 4. - Chaim Goodman-Strauss, Mar 31 2019
G.f.: (1 + 3*x + 6*x^2 + 6*x^3 + 10*x^4 + 12*x^5 + 12*x^6 + 18*x^7 + 7*x^8 + 6*x^10 + 3*x^11 + 12*x^12 + 12*x^13 - 12*x^16 - 6*x^17) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
a(n) = 2*a(n-4) - a(n-8) for n>17.
(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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