A313059 - OEIS

%I #7 Oct 21 2023 15:10:48

%S 1,4,9,14,18,23,29,32,37,44,45,50,59,59,64,74,72,77,89,86,91,104,99,

%T 104,119,113,118,134,126,131,149,140,145,164,153,158,179,167,172,194,

%U 180,185,209,194,199,224,207,212,239,221

%N Coordination sequence Gal.4.99.1 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_, Aug 28 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 > 10.

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