A315496 - OEIS

%I #6 Oct 21 2023 15:11:09

%S 1,6,11,16,22,28,34,40,45,50,56,62,67,72,78,84,90,96,101,106,112,118,

%T 123,128,134,140,146,152,157,162,168,174,179,184,190,196,202,208,213,

%U 218,224,230,235,240,246,252,258,264,269,274

%N Coordination sequence Gal.5.306.3 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 05 2021: (Start)

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

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

%K nonn

%O 0,2

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