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 A250122 Coordination sequence for planar net 3.12.12. 34
 1, 3, 4, 6, 8, 12, 14, 15, 18, 21, 22, 24, 28, 30, 30, 33, 38, 39, 38, 42, 48, 48, 46, 51, 58, 57, 54, 60, 68, 66, 62, 69, 78, 75, 70, 78, 88, 84, 78, 87, 98, 93, 86, 96, 108, 102, 94, 105, 118, 111, 102, 114, 128, 120, 110, 123, 138, 129 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also, growth series for group with presentation < S, T : S^2 = T^3 = (S*T)^6 = 1 >. See Magma program in A298805. - N. J. A. Sloane, Feb 06 2018 LINKS Maurizio Paolini, Table of n, a(n) for n = 0..1021 Agnes Azzolino, Regular and Semi-Regular Tessellation Paper, 2011 Agnes Azzolino, Illustration of 3.12.12 tiling [From previous link] Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers Chaim Goodman-Strauss and N. J. A. Sloane, A Coloring Book Approach to Finding Coordination Sequences, Acta Cryst. A75 (2019), 121-134, also on NJAS's home page. Also arXiv:1803.08530. Branko Grünbaum and Geoffrey C. Shephard, Tilings by regular polygons, Mathematics Magazine, 50 (1977), 227-247. Tom Karzes, Tiling Coordination Sequences Maurizio Paolini, C program for A250122 Reticular Chemistry Structure Resource, hca N. J. A. Sloane, The uniform planar nets and their A-numbers [Annotated scanned figure from Gruenbaum and Shephard (1977)] FORMULA From Joseph Myers, Nov 28 2014: (Start) Empirically, a(4n) = 10n - 2 except for a(0) = 1 a(4n+1) = 9n + 3 a(4n+2) = 8n + 6 except for a(2) = 4 a(4n+3) = 9n + 6. (End) If these are correct, the sequence has g.f. -(-1 - x - x^2 - 3*x^3 + x^4 - 5*x^5 + 3*x^6 - 4*x^7 + 2*x^8)/((x - 1)^2*(x^2 + 1)^2). - N. J. A. Sloane, Nov 28 2014 All the above conjectures are true. Details will be added soon. - N. J. A. Sloane, Dec 31 2015 MATHEMATICA Join[{1, 3, 4}, LinearRecurrence[{2, -3, 4, -3, 2, -1}, {6, 8, 12, 14, 15, 18}, 100]] (* Jean-François Alcover, Aug 05 2018 *) CROSSREFS List of coordination sequences for uniform planar nets: A008458 (the planar net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576 (4.8.8), A008579 (3.6.3.6), A008706 (3.3.3.4.4), A072154 (4.6.12), A219529 (3.3.4.3.4), A250120 (3.3.3.3.6), A250122 (3.12.12). Sequence in context: A050115 A167711 A037346 * A243653 A203444 A008864 Adjacent sequences:  A250119 A250120 A250121 * A250123 A250124 A250125 KEYWORD nonn AUTHOR Darrah Chavey, Nov 23 2014 EXTENSIONS a(8) onwards from Maurizio Paolini and Joseph Myers (independently), Nov 28 2014 STATUS approved

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Last modified November 23 21:51 EST 2020. Contains 338603 sequences. (Running on oeis4.)