

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
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OFFSET

1,2


COMMENTS

The layer sequence is the sequence of the cardinalities of the layers accumulating around a (finitesided) polygon of the tessellation under successive sidereflections; 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^26*x+1)
a(n) = A001109(n) + A001109(n1) + A001109(n2), 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



