A310683 - OEIS

%I #6 Oct 21 2023 15:10:34

%S 1,4,7,10,13,16,22,26,27,30,33,36,44,48,47,50,53,56,66,70,67,70,73,76,

%T 88,92,87,90,93,96,110,114,107,110,113,116,132,136,127,130,133,136,

%U 154,158,147,150,153,156,176,180

%N Coordination sequence Gal.4.15.3 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_, Dec 24 2019: (Start)

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

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

%K nonn

%O 0,2

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