A315431 - OEIS

%I #6 Oct 21 2023 15:11:09

%S 1,6,11,15,22,28,33,39,44,52,56,61,64,74,78,83,88,98,100,105,110,120,

%T 120,129,132,142,142,153,154,164,166,175,174,186,188,197,196,212,210,

%U 219,218,234,230,241,242,256,252,265,264,278

%N Coordination sequence Gal.6.669.6 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 From _Chai Wah Wu_, Dec 20 2019: (Start)

%F a(n) = a(n-4) - a(n-5) + a(n-7) + a(n-9) - a(n-11) + a(n-12) - a(n-16) for n > 22 (conjectured).

%F G.f.: (-x^22 - x^17 + x^16 + 8*x^15 + 11*x^14 + 16*x^13 + 21*x^12 + 23*x^11 + 30*x^10 + 34*x^9 + 31*x^8 + 34*x^7 + 28*x^6 + 23*x^5 + 21*x^4 + 15*x^3 + 11*x^2 + 6*x + 1)/(x^16 - x^12 + x^11 - x^9 - x^7 + x^5 - x^4 + 1) (conjectured). (End)

%K nonn

%O 0,2

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