A315823 - OEIS

%I #7 Oct 21 2023 15:11:10

%S 1,6,6,18,24,18,36,30,36,54,54,42,72,54,66,90,84,66,108,78,96,126,114,

%T 90,144,102,126,162,144,114,180,126,156,198,174,138,216,150,186,234,

%U 204,162,252,174,216,270,234,186,288,198

%N Coordination sequence Gal.6.507.3 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_, Apr 01 2023: (Start)

%F a(n) = 2*a(n-6) - a(n-12) for n > 12.

%F G.f.: (x^12 + 6*x^11 + 6*x^10 + 18*x^9 + 24*x^8 + 18*x^7 + 34*x^6 + 18*x^5 + 24*x^4 + 18*x^3 + 6*x^2 + 6*x + 1)/(x^12 - 2*x^6 + 1). (End)

%K nonn

%O 0,2

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