A312943 - OEIS

%I #7 Oct 21 2023 15:10:45

%S 1,4,9,13,18,23,27,32,36,40,45,49,54,59,63,68,72,76,81,85,90,95,99,

%T 104,108,112,117,121,126,131,135,140,144,148,153,157,162,167,171,176,

%U 180,184,189,193,198,203,207,212,216,220

%N Coordination sequence Gal.4.41.2 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_, Feb 14 2020: (Start)

%F a(n) = 2*a(n-1) - a(n-2) - a(n-4) + 2*a(n-5) - a(n-6) for n > 6.

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

%K nonn

%O 0,2

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