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%I #6 Oct 21 2023 15:11:10
%S 1,6,12,15,18,21,24,33,42,45,48,51,54,57,60,72,84,84,84,87,90,93,96,
%T 111,126,123,120,123,126,129,132,150,168,162,156,159,162,165,168,189,
%U 210,201,192,195,198,201,204,228,252,240
%N Coordination sequence Gal.6.609.6 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 From _Chai Wah Wu_, Dec 20 2019: (Start)
%F a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 7*a(n-6) + 8*a(n-7) - 7*a(n-8) + 6*a(n-9) - 5*a(n-10) + 4*a(n-11) - 3*a(n-12) + 2*a(n-13) - a(n-14) for n > 14 (conjectured).
%F G.f.: (x^14 + 4*x^13 + 3*x^12 + 5*x^11 + 5*x^10 + 6*x^9 + 7*x^8 + 13*x^7 + 7*x^6 + 6*x^5 + 5*x^4 + 5*x^3 + 3*x^2 + 4*x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^4 + 1)^2) (conjectured). (End)
%K nonn
%O 0,2
%A _Brian Galebach_ and _N. J. A. Sloane_, Jun 18 2018
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