A315001 - OEIS

%I #7 Apr 19 2024 02:00:35

%S 1,5,9,15,18,23,27,31,37,40,46,50,55,61,63,69,72,77,83,85,92,95,101,

%T 107,108,115,117,123,129,130,138,140,147,153,153,161,162,169,175,175,

%U 184,185,193,199,198,207,207,215,221,220

%N Coordination sequence Gal.6.190.4 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 18 2024: (Start)

%F a(n) = a(n-1) - a(n-2) + a(n-3) - 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) + a(n-11) - a(n-12) + a(n-13) - a(n-14) for n > 14.

%F G.f.: (x^2 + x + 1)*(x^12 + 3*x^11 + x^10 + 6*x^9 + x^8 + 7*x^7 + 7*x^5 + x^4 + 6*x^3 + x^2 + 3*x + 1)/((x - 1)^2*(x^4 - x^3 + x^2 - x + 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