The On-Line Encyclopedia of Integer Sequences (OEIS)

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A265067

Coordination sequence for (2,5,8) tiling of hyperbolic plane.
(history; published version)

#15 by Ray Chandler at Tue Feb 20 16:15:10 EST 2024

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editing

approved

#14 by Ray Chandler at Tue Feb 20 16:15:07 EST 2024

LINKS

<a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 1, 1, 2, 1, 2, 1, 1, 0, 0, -1).

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approved

editing

#13 by Alois P. Heinz at Mon Aug 07 11:42:35 EDT 2017

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proposed

approved

#12 by G. C. Greubel at Mon Aug 07 11:31:58 EDT 2017

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editing

proposed

#11 by G. C. Greubel at Mon Aug 07 11:31:51 EDT 2017

LINKS

G. C. Greubel, <a href="/A265067/b265067.txt">Table of n, a(n) for n = 0..1000</a>

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approved

editing

#10 by Bruno Berselli at Wed Jan 20 02:55:10 EST 2016

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proposed

approved

#9 by Vincenzo Librandi at Wed Jan 20 01:39:39 EST 2016

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editing

proposed

#8 by Vincenzo Librandi at Wed Jan 20 01:39:24 EST 2016

FORMULA

G.f.: (Xx+1)^2*(Xx^4+Xx^3+Xx^2+Xx+1)*(Xx^6+Xx^4+Xx^2+1)/(Xx^12-Xx^9-Xx^8-2*Xx^7-Xx^6-2*Xx^5-Xx^4-Xx^3+1).

MATHEMATICA

CoefficientList[Series[(x + 1)^2 (x^4 + x^3 + x^2 + x + 1) (x^6 + x^4 + x^2 + 1) / (x^12 - x^9 - x^8 - 2 x^7 - x^6 - 2 x^5 - x^4 - x^3 + 1), {x, 0, 45}], x] (* Vincenzo Librandi, Jan 20 2016 *)

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proposed

editing

#7 by Michel Marcus at Wed Jan 20 01:08:09 EST 2016

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editing

proposed

#6 by Michel Marcus at Wed Jan 20 01:08:05 EST 2016

REFERENCES

J. W. Cannon, P. Wagreich, Growth functions of surface groups, Mathematische Annalen, 1992, Volume 293, pp. 239-257. See Prop. 3.1.

LINKS

J. W. Cannon, P. Wagreich, <a href="http://dx.doi.org/10.1007/BF01444714">Growth functions of surface groups</a>, Mathematische Annalen, 1992, Volume 293, pp. 239-257. See Prop. 3.1.

PROG

(PARI) Vec((x+1)^2*(x^4+x^3+x^2+x+1)*(x^6+x^4+x^2+1)/(x^12-x^9-x^8-2*x^7-x^6-2*x^5-x^4-x^3+1) + O(x^50)) \\ Michel Marcus, Jan 20 2016

STATUS

approved

editing