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%I #14 Feb 08 2023 09:39:34
%S 1,3,6,11,20,36,64,113,200,354,626,1107,1958,3464,6128,10839,19172,
%T 33913,59988,106111,187696,332009,587280,1038820,1837534,3250353,
%U 5749442,10169998,17989372,31820803,56286764,99563792,176115092
%N Layer counting sequence for hyperbolic tessellation by cuspidal triangles of angles (Pi/3, Pi/5, Pi/7).
%C 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.
%H G. C. Greubel, <a href="/A054887/b054887.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Con#coordseqs">Index entries for Coordination Sequences</a> [A layer sequence is a kind of coordination sequence. - _N. J. A. Sloane_, Nov 20 2022]
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,2,4,3,4,2,2,0,0,-1).
%F 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).
%t 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 *)
%o (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
%o (Sage)
%o def A054887_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o 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()
%o a=A054887_list(40); a[1:] # _G. C. Greubel_, Feb 07 2023
%Y Cf. A054888.
%K nonn
%O 1,2
%A Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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