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A054890 Layer counting sequence for hyperbolic tessellation by regular heptagons of angle Pi/3. 1
1, 7, 42, 245, 1428, 8323, 48510, 282737, 1647912, 9604735, 55980498, 326278253, 1901689020, 11083855867, 64601446182, 376524821225, 2194547481168, 12790760065783, 74550012913530, 434509317415397 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The layer sequence is the sequence of the cardinalities of the layers accumulating around a (finite-sided) polygon of the tessellation under successive side-reflections; see the illustration accompanying A054888.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..1307

Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.

Index entries for Coordination Sequences [A layer sequence is a kind of coordination sequence. - N. J. A. Sloane, Nov 20 2022]

Index entries for linear recurrences with constant coefficients, signature (6,-1).

FORMULA

G.f.: (x^2+x+1)/(x^2-6*x+1)

a(n) = A001109(n) + A001109(n-1) + A001109(n-2), n>1. - Ralf Stephan, Apr 26 2003

MATHEMATICA

CoefficientList[Series[(x^2 + x + 1)/(x^2 - 6 x + 1), {x, 0, 19}], x] (* Michael De Vlieger, Dec 29 2020 *)

LinearRecurrence[{6, -1}, {1, 7, 42}, 20] (* Harvey P. Dale, Jun 06 2021 *)

CROSSREFS

{a(n)/7} for n>1 is A001109.

Sequence in context: A111995 A050152 A030240 * A102594 A053142 A214941

Adjacent sequences: A054887 A054888 A054889 * A054891 A054892 A054893

KEYWORD

nonn,changed

AUTHOR

Paolo Dominici (pl.dm(AT)libero.it), May 23 2000

STATUS

approved

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Last modified November 30 12:40 EST 2022. Contains 358441 sequences. (Running on oeis4.)