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A265075
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Coordination sequence for (3,4,4) tiling of hyperbolic plane.
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27
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1, 3, 6, 11, 18, 29, 46, 73, 116, 183, 290, 459, 726, 1149, 1818, 2877, 4552, 7203, 11398, 18035, 28538, 45157, 71454, 113065, 178908, 283095, 447954, 708819, 1121598, 1774757, 2808282, 4443677, 7031440, 11126179, 17605478, 27857979, 44080994, 69751437, 110370990, 174645225, 276349380, 437280663, 691929826
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OFFSET
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0,2
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LINKS
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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.
M. O'Keeffe, Coordination sequences for hyperbolic tilings, Zeitschrift für Kristallographie, 213 (1998), 135-140 (see last table, row 6.8.8H).
Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,1,0,1,-1).
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FORMULA
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G.f.: (x^3+x^2+x+1)*(x^2+x+1)*(x+1)/(x^6-x^4-2*x^3-x^2+1).
a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)-a(n-8) for n>8. - Vincenzo Librandi, Dec 30 2015
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MATHEMATICA
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CoefficientList[Series[(x^3 + x^2 + x + 1) (x^2 + x + 1) (x + 1)/(x^6 - x^4 - 2 x^3 - x^2 + 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)
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PROG
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(Magma) I:=[1, 3, 6, 11, 18, 29, 46, 73, 116]; [n le 9 select I[n] else Self(n-1)+Self(n-3)+Self(n-5) + Self(n-7)-Self(n-8): 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^4-2*x^3-x^2+1)) \\ G. C. Greubel, Aug 07 2017
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CROSSREFS
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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: A286272 A212147 A066778 * A147079 A281572 A152074
Adjacent sequences: A265072 A265073 A265074 * A265076 A265077 A265078
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Dec 29 2015
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STATUS
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approved
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