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Coordination sequence Gal.4.36.1 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 #6 Oct 21 2023 15:10:32

%S 1,3,6,10,13,16,19,20,26,35,34,31,34,46,51,46,49,56,62,61,62,69,72,76,

%T 79,82,83,84,92,99,100,97,100,110,115,112,113,122,128,127,126,133,138,

%U 140,145,148,149,148,156,165

%N Coordination sequence Gal.4.36.1 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_, Dec 24 2019: (Start)

%F a(n) = - a(n-2) + a(n-5) + 2*a(n-7) + a(n-9) - a(n-12) - a(n-14) for n > 16.

%F G.f.: (-2*x^16 + x^14 + 3*x^13 + 7*x^12 + 15*x^11 + 21*x^10 + 29*x^9 + 29*x^8 + 28*x^7 + 29*x^6 + 25*x^5 + 19*x^4 + 13*x^3 + 7*x^2 + 3*x + 1)/(x^14 + x^12 - x^9 - 2*x^7 - x^5 + x^2 + 1). (End)

%K nonn

%O 0,2

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