A313297 - OEIS

%I #6 Oct 21 2023 15:10:49

%S 1,4,9,15,21,27,33,39,45,51,57,62,66,70,75,81,87,93,99,105,111,117,

%T 123,128,132,136,141,147,153,159,165,171,177,183,189,194,198,202,207,

%U 213,219,225,231,237,243,249,255,260,264,268

%N Coordination sequence Gal.6.210.1 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_, Mar 22 2021: (Start)

%F a(n) = 3*a(n-1) - 4*a(n-2) + 3*a(n-3) - a(n-4) - a(n-6) + 3*a(n-7) - 4*a(n-8) + 3*a(n-9) - a(n-10) for n > 10.

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

%K nonn

%O 0,2

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