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
G. C. Greubel, Table of n, a(n) for n = 1..1000
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 (0,0,2,2,4,3,4,2,2,0,0,-1).
FORMULA
G.f.: x*(1+x)*(1-x^3)*(1-x^5)*(1-x^7)/(1-2*x+x^4+x^6-x^10-x^12+2*x^15-x^16).
MATHEMATICA
LinearRecurrence[{0, 0, 2, 2, 4, 3, 4, 2, 2, 0, 0, -1}, {1, 3, 6, 11, 20, 36, 64, 113, 200, 354, 626, 1107, 1958}, 41] (* G. C. Greubel, Feb 07 2023 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1+x)*(1-x^3)*(1-x^5)*(1-x^7)/(1-2*x+x^4+x^6-x^10-x^12+2*x^15-x^16) )); // G. C. Greubel, Feb 07 2023
(Sage)
def A054887_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1+x)*(1-x^3)*(1-x^5)*(1-x^7)/(1-2*x+x^4+x^6-x^10-x^12+2*x^15-x^16) ).list()
a=A054887_list(40); a[1:] # G. C. Greubel, Feb 07 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
STATUS
approved