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Coordination sequence Gal.4.111.3 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
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%I #7 Oct 21 2023 15:11:10

%S 1,6,6,18,12,30,24,30,42,30,60,42,54,66,48,90,60,78,90,66,120,78,102,

%T 114,84,150,96,126,138,102,180,114,150,162,120,210,132,174,186,138,

%U 240,150,198,210,156,270,168,222,234,174

%N Coordination sequence Gal.4.111.3 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

%C Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

%H Brian Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>

%F Conjectures from _Chai Wah Wu_, Dec 28 2021: (Start)

%F a(n) = 2*a(n-5) - a(n-10) for n > 10.

%F G.f.: (x^10 + 6*x^9 + 6*x^8 + 18*x^7 + 12*x^6 + 28*x^5 + 12*x^4 + 18*x^3 + 6*x^2 + 6*x + 1)/(x^10 - 2*x^5 + 1). (End)

%K nonn

%O 0,2

%A _Brian Galebach_ and _N. J. A. Sloane_, Jun 18 2018