A314829 - OEIS

%I #7 Oct 21 2023 15:11:03

%S 1,5,9,14,18,22,27,31,36,41,45,50,54,58,63,67,72,77,81,86,90,94,99,

%T 103,108,113,117,122,126,130,135,139,144,149,153,158,162,166,171,175,

%U 180,185,189,194,198,202,207,211,216,221

%N Coordination sequence Gal.4.41.3 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_, Jun 08 2022: (Start)

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

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

%K nonn

%O 0,2

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