A313577 - OEIS

%I #7 Apr 16 2024 02:38:09

%S 1,5,10,14,19,25,29,35,39,42,51,52,59,64,65,77,76,84,88,89,102,99,109,

%T 112,113,128,123,133,137,136,153,147,157,162,160,179,170,182,186,183,

%U 205,193,207,211,207,230,217,231,235,231

%N Coordination sequence Gal.4.97.3 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 16 2024: (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) + 2*a(n-9) + a(n-10) + a(n-11) + a(n-12) + a(n-13) - a(n-14) - a(n-15) - a(n-16) - a(n-17) - a(n-18) for n > 18.

%F G.f.: (x + 1)^2*(x^16 + 4*x^15 + 7*x^14 + 12*x^13 + 18*x^12 + 24*x^11 + 25*x^10 + 32*x^9 + 28*x^8 + 32*x^7 + 25*x^6 + 24*x^5 + 18*x^4 + 12*x^3 + 7*x^2 + 4*x + 1)/((x - 1)^2*(x^2 + x + 1)*(x^6 + x^3 + 1)*(x^4 + x^3 + x^2 + x + 1)^2). (End)

%K nonn

%O 0,2

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