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 A265071 Coordination sequence for (3,3,4) tiling of hyperbolic plane. 27
 1, 3, 6, 10, 15, 22, 31, 44, 62, 87, 122, 171, 240, 336, 471, 660, 925, 1296, 1816, 2545, 3566, 4997, 7002, 9812, 13749, 19266, 26997, 37830, 53010, 74281, 104088, 145855, 204382, 286394, 401315, 562350, 788003, 1104204, 1547286, 2168163, 3038178, 4257303, 5965624, 8359440, 11713819, 16414204, 23000705, 32230160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 J. W. Cannon, P. Wagreich, Growth functions of surface groups, Mathematische Annalen, 1992, Volume 293, pp. 239-257. See Prop. 3.1. Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,0,-1). FORMULA G.f.: (x^3+x^2+x+1)*(x^2+x+1)*(x+1)/(x^6-x^4-x^3-x^2+1). a(n) = a(n-2)+a(n-3)+a(n-4)-a(n-6) for n>6. - Vincenzo Librandi, Dec 30 2015 MATHEMATICA CoefficientList[Series[(x^3 + x^2 + x + 1) (x^2 + x + 1) (x + 1)/(x^6 - x^4 - x^3 - x^2 + 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *) PROG (Magma) I:=[1, 3, 6, 10, 15, 22, 31]; [n le 7 select I[n] else Self(n-2)+Self(n-3)+Self(n-4)- Self(n-6): n in [1..50]]; // Vincenzo Librandi, Dec 30 2015 (PARI) x='x+O('x^50); Vec((x^3+x^2+x+1)*(x^2+x+1)*(x+1)/(x^6-x^4-x^3-x^2+1)) \\ G. C. Greubel, Aug 07 2017 CROSSREFS Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077. Sequence in context: A173645 A122047 A177100 * A330910 A226239 A209231 Adjacent sequences: A265068 A265069 A265070 * A265072 A265073 A265074 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 29 2015 STATUS approved

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Last modified April 24 02:43 EDT 2024. Contains 371917 sequences. (Running on oeis4.)