A310668 - OEIS

%I #6 Oct 21 2023 15:10:34

%S 1,4,6,9,12,16,20,22,27,31,30,35,40,44,47,45,51,59,60,60,63,70,73,75,

%T 78,80,86,88,91,97,96,99,106,110,111,111,117,123,126,126,127,136,139,

%U 139,144,146,150,154,157,161

%N Coordination sequence Gal.4.30.2 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 24 2019: (Start)

%F a(n) = - a(n-2) + a(n-3) + 2*a(n-5) + a(n-7) - a(n-8) - a(n-10) for n > 12.

%F G.f.: (-3*x^12 + x^10 + 7*x^9 + 10*x^8 + 13*x^7 + 15*x^6 + 17*x^5 + 14*x^4 + 12*x^3 + 7*x^2 + 4*x + 1)/(x^10 + x^8 - x^7 - 2*x^5 - x^3 + x^2 + 1). (End)

%K nonn

%O 0,2

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