A315540 - OEIS

%I #7 Oct 21 2023 15:11:10

%S 1,6,11,17,23,29,34,39,45,51,57,62,68,74,79,85,91,97,102,107,113,119,

%T 125,130,136,142,147,153,159,165,170,175,181,187,193,198,204,210,215,

%U 221,227,233,238,243,249,255,261,266,272,278

%N Coordination sequence Gal.6.643.4 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 21 2021: (Start)

%F a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - 2*a(n-8) + 2*a(n-9) - 2*a(n-10) + 2*a(n-11) - a(n-12) for n > 12.

%F G.f.: (x^12 + 4*x^11 + x^10 + 5*x^9 + x^8 + 5*x^7 + 5*x^5 + x^4 + 5*x^3 + x^2 + 4*x + 1)/((x - 1)^2*(x^2 + 1)*(x^2 - x + 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