A315418 - OEIS

%I #10 Jul 11 2025 08:49:12

%S 1,6,11,15,20,26,32,37,41,46,52,58,63,67,72,78,84,89,93,98,104,110,

%T 115,119,124,130,136,141,145,150,156,162,167,171,176,182,188,193,197,

%U 202,208,214,219,223,228,234,240,245,249,254

%N Coordination sequence Gal.3.21.3 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_, Jul 10 2025: (Start)

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

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

%F Conjecture: a(n) ~ 26*n/5. - _Stefano Spezia_, Jul 11 2025

%K nonn

%O 0,2

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