A315317 - OEIS

%I #6 Oct 21 2023 15:11:08

%S 1,6,10,16,21,25,32,37,41,48,52,56,64,68,72,80,83,87,96,99,103,112,

%T 114,118,128,130,134,144,145,149,160,161,165,176,176,180,192,192,196,

%U 208,207,211,224,223,227,240,238,242,256,254

%N Coordination sequence Gal.5.257.3 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 19 2020: (Start)

%F a(n) = a(n-1) - a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) + a(n-7) - a(n-8) for n > 8.

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

%K nonn

%O 0,2

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