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
a(n) = 7*A001109(n-1) + [n=1].
G.f.: x*(1+x+x^2)/(1-6*x+x^2).
MATHEMATICA
Rest@CoefficientList[Series[x*(1+x+x^2)/(1-6*x+x^2), {x, 0, 30}], x] (* Michael De Vlieger, Dec 29 2020 *)
LinearRecurrence[{6, -1}, {1, 7, 42}, 20] (* Harvey P. Dale, Jun 06 2021 *)
PROG
(Magma) [n eq 1 select 1 else 7*Evaluate(ChebyshevSecond(n-1), 3): n in [1..40]]; // G. C. Greubel, Feb 08 2023
(SageMath) [7*chebyshev_U(n-2, 3) + int(n==1) for n in range(1, 41)] # G. C. Greubel, Feb 08 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
STATUS
approved