A312956 - OEIS

%I #6 Oct 21 2023 15:10:46

%S 1,4,9,13,18,24,26,31,36,40,45,52,52,58,63,67,72,80,78,85,90,94,99,

%T 108,104,112,117,121,126,136,130,139,144,148,153,164,156,166,171,175,

%U 180,192,182,193,198,202,207,220,208,220

%N Coordination sequence Gal.5.264.1 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-6) - a(n-12) for n > 12.

%F G.f.: (x^12 + 4*x^11 + 9*x^10 + 14*x^9 + 18*x^8 + 23*x^7 + 24*x^6 + 24*x^5 + 18*x^4 + 13*x^3 + 9*x^2 + 4*x + 1)/(x^12 - 2*x^6 + 1). (End)

%K nonn

%O 0,2

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