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Coordination sequence Gal.5.41.2 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 #8 Oct 21 2023 15:10:32

%S 1,3,5,8,11,14,18,21,23,25,28,32,34,35,39,44,47,48,50,55,58,58,61,66,

%T 69,71,74,78,80,81,85,89,90,92,97,102,103,103,108,113,113,114,119,124,

%U 126,127,131,135,136,138

%N Coordination sequence Gal.5.41.2 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 10 2018: (Start)

%F a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-19) - a(n-20) + a(n-21) - a(n-22) for n > 22.

%F G.f.: (x + 1)^2*(x^2 - x + 1)^2*(x^2 + x + 1)*(x^14 + x^13 + x^12 + x^11 - x^10 + x^8 + x^7 + x^6 - x^4 + x^3 + x^2 + x + 1)/(x^22 - x^21 + x^20 - x^19 - x^3 + x^2 - x + 1). (End)

%K nonn

%O 0,2

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