login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 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

AUTHOR

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 05:42 EST 2021. Contains 349426 sequences. (Running on oeis4.)