A314121 - OEIS

%I #7 Apr 19 2024 02:00:37

%S 1,5,11,16,21,26,32,38,42,48,54,58,64,70,75,80,85,91,96,101,107,112,

%T 117,122,128,134,138,144,150,154,160,166,171,176,181,187,192,197,203,

%U 208,213,218,224,230,234,240,246,250,256,262

%N Coordination sequence Gal.6.657.6 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 17 2024: (Start)

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

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

%K nonn

%O 0,2

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