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A310936 Coordination sequence Gal.3.7.3 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. 0

%I #6 Oct 21 2023 15:10:35

%S 1,4,7,8,8,10,17,24,28,28,27,28,32,40,47,48,46,48,55,60,62,64,65,64,

%T 66,76,85,84,80,84,93,96,96,100,103,100,100,112,123,120,114,120,131,

%U 132,130,136,141,136,134,148

%N Coordination sequence Gal.3.7.3 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_, Mar 11 2021: (Start)

%F a(n) = 3*a(n-1) - 5*a(n-2) + 6*a(n-3) - 5*a(n-4) + 3*a(n-5) - 2*a(n-6) + 3*a(n-7) - 5*a(n-8) + 6*a(n-9) - 5*a(n-10) + 3*a(n-11) - a(n-12) for n > 17.

%F G.f.: (-2*x^17 + 2*x^16 - 2*x^15 + 2*x^14 + 3*x^12 - x^11 + 2*x^10 - 3*x^9 + 4*x^8 - x^7 + 4*x^6 + x^5 + x^3 + x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^2 - x + 1)*(x^4 - x^2 + 1)). (End)

%K nonn

%O 0,2

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

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Last modified July 13 11:10 EDT 2024. Contains 374282 sequences. (Running on oeis4.)