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Coordination sequence Gal.4.65.1 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 15:10:36

%S 1,4,8,12,18,22,26,32,36,38,44,50,50,58,64,68,66,76,82,78,90,96,100,

%T 94,108,114,106,122,128,132,122,140,146,134,154,160,164,150,172,178,

%U 162,186,192,196,178,204,210,190,218,224

%N Coordination sequence Gal.4.65.1 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_, Jan 24 2020: (Start)

%F a(n) = 2*a(n-7) - a(n-14) for n > 16.

%F G.f.: (-2*x^16 + x^14 + 6*x^13 + 6*x^12 + 14*x^11 + 20*x^10 + 22*x^9 + 28*x^8 + 30*x^7 + 26*x^6 + 22*x^5 + 18*x^4 + 12*x^3 + 8*x^2 + 4*x + 1)/(x^14 - 2*x^7 + 1). (End)

%K nonn

%O 0,2

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