A310019 - OEIS

%I #8 Oct 21 2023 15:10:32

%S 1,3,5,10,17,21,20,19,23,34,45,45,38,39,45,52,63,71,68,59,59,72,87,91,

%T 88,87,85,88,101,113,114,109,107,112,123,129,130,133,135,136,141,149,

%U 152,151,153,162,171,169,166,171

%N Coordination sequence Gal.6.110.1 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_, Dec 10 2018: (Start)

%F a(n) = a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) + 2*a(n-7) - a(n-8) + 2*a(n-9) - 2*a(n-10) + 2*a(n-11) - 2*a(n-12) + a(n-13) - a(n-14) for n > 16.

%F G.f.: (-2*x^16 + 2*x^15 - x^14 + 4*x^13 + 4*x^12 + 11*x^11 + 15*x^10 + 18*x^9 + 16*x^8 + 18*x^7 + 18*x^6 + 18*x^5 + 13*x^4 + 9*x^3 + 4*x^2 + 2*x + 1)/((x - 1)^2*(x^2 + 1)*(x^2 - x + 1)*(x^2 + x + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). (End)

%K nonn

%O 0,2

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