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
Georg Fischer, Table of n, a(n) for n = 1..500
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 (3,1,3,-1).
FORMULA
G.f.: x*(1+2*x+4*x^2+2*x^3+x^4)/(1-3*x-x^2-3*x^3+x^4).
MATHEMATICA
LinearRecurrence[{3, 1, 3, -1}, {1, 5, 20, 70, 245}, 40] (* Georg Fischer, Apr 13 2020 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1+2*x+4*x^2+2*x^3+x^4)/(1-3*x-x^2-3*x^3+x^4) )); // G. C. Greubel, Feb 08 2023
(Sage)
def A054889_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1+2*x+4*x^2+2*x^3+x^4)/(1-3*x-x^2-3*x^3+x^4) ).list()
a=A054889_list(40); a[1:] # G. C. Greubel, Feb 08 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
EXTENSIONS
a(21) inserted by Georg Fischer, Apr 13 2020
STATUS
approved