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A310025 Coordination sequence Gal.4.31.2 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.

%I A310025 #8 Oct 21 2023 15:10:32
%S A310025 1,3,5,8,10,15,18,19,22,25,28,31,34,38,39,41,46,47,49,54,58,61,60,63,
%T A310025 70,69,70,77,82,84,81,85,94,91,91,100,106,107,102,107,118,113,112,123,
%U A310025 130,130,123,129,142,135
%N A310025 Coordination sequence Gal.4.31.2 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 A310025 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 A310025 Brian Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>
%F A310025 Conjectures from _Chai Wah Wu_, Dec 10 2018: (Start)
%F A310025 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 > 16.
%F A310025 G.f.: (-2*x^16 + 4*x^15 - 3*x^14 + 5*x^13 - 4*x^12 + 11*x^11 - 4*x^10 + 12*x^9 - 2*x^8 + 11*x^7 + 8*x^5 + 2*x^4 + 3*x^3 + 2*x^2 + x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^4 + 1)^2). (End)
%K A310025 nonn
%O A310025 0,2
%A A310025 _Brian Galebach_ and _N. J. A. Sloane_, Jun 18 2018