login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Coordination sequence Gal.3.7.1 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.
0

%I #6 Oct 21 2023 15:10:32

%S 1,3,5,9,12,15,17,19,24,29,31,33,36,39,41,45,50,51,51,55,62,65,65,69,

%T 74,75,75,81,88,87,85,91,100,101,99,105,112,111,109,117,126,123,119,

%U 127,138,137,133,141,150,147

%N Coordination sequence Gal.3.7.1 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 24 2019: (Start)

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

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

%K nonn

%O 0,2

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