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 A307270 Coordination sequence for trivalent node of type alpha''' in the first Moore pentagonal tiling. 7
 1, 3, 6, 9, 13, 18, 27, 31, 34, 41, 50, 58, 61, 64, 75, 81, 82, 85, 100, 104, 103, 106, 125, 127, 124, 127, 150, 150, 145, 148, 175, 173, 166, 169, 200, 196, 187, 190, 225, 219, 208, 211, 250, 242, 229, 232, 275, 265, 250, 253, 300, 288, 271, 274, 325, 311 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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). The group is p3m1. - Davide M. Proserpio, Apr 01 2019 REFERENCES Herbert C. Moore, U.S. Patent 928,320, Patented July 20 1909. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..1000 Davide M. Proserpio, Another drawing of the first Moore tiling {Labels: V1 = alpha'''', V2 = alpha''', V3 = alpha'', V4 = beta, V5 = alpha', V6 = alpha] Rémy Sigrist, Illustration of first terms Rémy Sigrist, PARI program for A307270 N. J. A. Sloane, The first Moore tiling [Constructed by copy-and-paste from the illustration in the patent] N. J. A. Sloane, Fundamental cell FORMULA For n >= 10, a(n+4) = a(n) + [21,21,25,23] according as n == [0,1,2,3] mod 4. - Chaim Goodman-Strauss, Mar 31 2019 Conjectures from Colin Barker, Apr 03 2019: (Start) G.f.: (1 + 3*x + 6*x^2 + 9*x^3 + 11*x^4 + 12*x^5 + 15*x^6 + 13*x^7 + 9*x^8 + 8*x^9 + 2*x^10 + 5*x^11 + 6*x^12 + 2*x^14 - 4*x^15 - 6*x^16 - 2*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) PROG (PARI) See Links section. CROSSREFS Cf. A307201-A307205, A307270, A307271-A307276. Sequence in context: A059293 A002578 A129728 * A310160 A117469 A073359 Adjacent sequences:  A307267 A307268 A307269 * A307271 A307272 A307273 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 30 2019 EXTENSIONS Terms a(7)-a(20) (and a corrected a(6)) from Davide M. Proserpio using ToposPro, Apr 01 2019 More terms from Rémy Sigrist, Apr 02 2019 STATUS approved

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Last modified July 17 18:47 EDT 2019. Contains 325109 sequences. (Running on oeis4.)