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Coordination sequence Gal.6.234.5 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 #6 Oct 21 2023 15:11:09

%S 1,6,11,16,21,25,29,33,38,43,48,54,60,65,70,75,79,83,87,92,97,102,108,

%T 114,119,124,129,133,137,141,146,151,156,162,168,173,178,183,187,191,

%U 195,200,205,210,216,222,227,232,237,241

%N Coordination sequence Gal.6.234.5 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_, Jul 27 2022: (Start)

%F a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.

%F G.f.: (x^12 + 5*x^11 + 5*x^10 + 5*x^9 + 5*x^8 + 4*x^7 + 4*x^6 + 4*x^5 + 5*x^4 + 5*x^3 + 5*x^2 + 5*x + 1)/(x^12 - x^11 - x + 1). (End)

%K nonn

%O 0,2

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