A313921 - OEIS

%I #6 Oct 21 2023 15:10:55

%S 1,5,10,16,22,27,34,41,46,52,56,59,66,73,78,84,90,95,102,109,112,116,

%T 122,127,134,141,146,152,158,163,168,173,178,184,190,195,202,209,214,

%U 220,224,227,234,241,246,252,258,263,270,277

%N Coordination sequence Gal.5.313.2 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 09 2023: (Start)

%F a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 6*a(n-6) + 6*a(n-7) - 6*a(n-8) + 6*a(n-9) - 5*a(n-10) + 4*a(n-11) - 3*a(n-12) + 2*a(n-13) - a(n-14) for n > 14.

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

%K nonn

%O 0,2

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