A310018 - OEIS

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

%S 1,3,5,10,14,17,17,20,27,33,36,40,39,39,44,55,65,64,60,61,65,72,83,91,

%T 84,82,87,93,100,109,111,106,108,115,121,126,129,133,132,136,143,147,

%U 146,151,159,160,164,169,167,168

%N Coordination sequence Gal.4.34.1 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-6) + a(n-7) - a(n-13) for n > 23.

%F G.f.: (-2*x^23 - 4*x^22 + 2*x^20 - 2*x^18 + 2*x^17 + 6*x^16 + 3*x^13 + 5*x^12 + 9*x^11 + 12*x^10 + 18*x^9 + 19*x^8 + 16*x^7 + 16*x^6 + 17*x^5 + 14*x^4 + 10*x^3 + 5*x^2 + 3*x + 1)/(x^13 - x^7 - x^6 + 1). (End)

%K nonn

%O 0,2

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