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 A298036 Coordination sequence of Dual(4.6.12) tiling with respect to a 12-valent node. 23
 1, 12, 12, 36, 24, 60, 36, 84, 48, 108, 60, 132, 72, 156, 84, 180, 96, 204, 108, 228, 120, 252, 132, 276, 144, 300, 156, 324, 168, 348, 180, 372, 192, 396, 204, 420, 216, 444, 228, 468, 240, 492, 252, 516, 264, 540, 276, 564, 288, 588, 300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Conjecture: For n>0, a(n)=6n if n even, otherwise 12n. The conjecture can easily be shown to be true: The vertices at distance 2k consist of 3k 12-valent and 3k 4-alent vertices, and the vertices at distance 2k+1 consist of 6(k+1) 6-valent and 6(k+1) 4-valent vertices. - Charlie Neder, Apr 22 2019 LINKS Hakan Icoz, Table of n, a(n) for n = 0..20000 Tom Karzes, Tiling Coordination Sequences N. J. A. Sloane, Illustration of initial terms (shows one 60-degree sector of tiling) N. J. A. Sloane, Overview of coordination sequences of Laves tilings [Fig. 2.7.1 of Grünbaum-Shephard 1987 with A-numbers added and in some cases the name in the RCSR database] FORMULA From Charlie Neder, Apr 22 2019: (Start) a(n) = 6 * n * (1 + n mod 2), n > 0. G.f.: (1 + 12*x + 10*x^2 + 12*x^3 + x^4)/(1 - x^2)^2. (End) CROSSREFS Cf. A072154, A298037 (partial sums), A298038 (hexavalent node), A298040 (tetravalent node). Cf. A109043 (a(n)/6), A026741 (a(n)/12). List of coordination sequences for Laves tilings (or duals of uniform planar nets): [3,3,3,3,3.3] = A008486; [3.3.3.3.6] = A298014, A298015, A298016; [3.3.3.4.4] = A298022, A298024; [3.3.4.3.4] = A008574, A296368; [3.6.3.6] = A298026, A298028; [3.4.6.4] = A298029, A298031, A298033; [3.12.12] = A019557, A298035; [4.4.4.4] = A008574; [4.6.12] = A298036, A298038, A298040; [4.8.8] = A022144, A234275; [6.6.6] = A008458. Sequence in context: A070710 A048759 A303646 * A119877 A307842 A147833 Adjacent sequences:  A298033 A298034 A298035 * A298037 A298038 A298039 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 22 2018 EXTENSIONS a(7)-a(50) from Charlie Neder, Apr 22 2019 STATUS approved

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)