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Coordination sequence Gal.6.200.3 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.
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%I #7 Oct 21 2023 15:10:53

%S 1,5,10,15,20,26,31,36,42,47,52,57,62,67,72,77,82,88,93,98,104,109,

%T 114,119,124,129,134,139,144,150,155,160,166,171,176,181,186,191,196,

%U 201,206,212,217,222,228,233,238,243,248,253

%N Coordination sequence Gal.6.200.3 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_, Oct 20 2023: (Start)

%F a(n) = a(n-1) + a(n-3) - a(n-4) - a(n-6) + a(n-7) + a(n-9) - a(n-10) for n > 10.

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

%K nonn

%O 0,2

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