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Coordination sequence Gal.4.51.1 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 #9 Oct 21 2023 15:10:36

%S 1,4,8,12,17,22,27,32,36,38,41,46,52,58,63,68,69,71,75,81,89,94,99,

%T 100,102,105,110,119,125,130,130,133,136,140,149,155,161,160,163,167,

%U 171,180,185,191,190,193,197,202,212,216

%N Coordination sequence Gal.4.51.1 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_, Jan 24 2020: (Start)

%F a(n) = - a(n-2) - a(n-4) - a(n-6) + 2*a(n-7) + 2*a(n-9) + 2*a(n-11) + 2*a(n-13) - a(n-14) - a(n-16) - a(n-18) - a(n-20) for n > 20.

%F G.f.: (x^20 + 4*x^19 + 9*x^18 + 17*x^17 + 26*x^16 + 38*x^15 + 53*x^14 + 68*x^13 + 80*x^12 + 86*x^11 + 89*x^10 + 86*x^9 + 80*x^8 + 68*x^7 + 53*x^6 + 38*x^5 + 26*x^4 + 16*x^3 + 9*x^2 + 4*x + 1)/((x - 1)^2*(x^2 + 1)*(x^4 + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)^2). (End)

%K nonn

%O 0,2

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