A314400 - OEIS

%I #6 Oct 21 2023 15:10:58

%S 1,5,8,11,20,23,26,31,36,41,42,49,56,59,60,65,74,75,78,85,92,95,94,

%T 101,110,113,112,119,130,129,128,137,148,149,146,155,166,165,162,173,

%U 186,183,180,191,202,201,198,209,222,219

%N Coordination sequence Gal.6.392.6 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_, Jan 12 2023: (Start)

%F a(n) = - a(n-2) + a(n-3) + 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-15) - a(n-16) - a(n-18) for n > 18.

%F G.f.: (x^18 + 5*x^17 + 9*x^16 + 15*x^15 + 23*x^14 + 25*x^13 + 31*x^12 + 30*x^11 + 32*x^10 + 32*x^9 + 32*x^8 + 30*x^7 + 31*x^6 + 25*x^5 + 23*x^4 + 15*x^3 + 9*x^2 + 5*x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^2 + x + 1)*(x^4 - x^2 + 1)*(x^6 + x^5 + 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