A313217 - OEIS

%I #7 Jun 06 2024 14:32:18

%S 1,4,9,15,19,25,32,35,40,46,50,54,62,67,69,76,81,84,91,99,101,104,112,

%T 115,119,128,134,135,140,148,150,155,164,168,169,176,184,185,191,200,

%U 202,204,213,219,219,227,235,236,241,250

%N Coordination sequence Gal.6.382.4 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_, Jun 06 2024: (Start)

%F a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 5*a(n-5) - 4*a(n-6) + 4*a(n-7) - 4*a(n-8) + 4*a(n-9) - 4*a(n-10) + 5*a(n-11) - 5*a(n-12) + 4*a(n-13) - 3*a(n-14) + 2*a(n-15) - a(n-16) for n > 19.

%F G.f.: (-x^19 + x^18 - x^17 + 2*x^16 + x^15 + 6*x^14 + 2*x^13 + 10*x^12 + 6*x^11 + 13*x^10 + 9*x^9 + 10*x^8 + 12*x^7 + 8*x^6 + 11*x^5 + 5*x^4 + 5*x^3 + 4*x^2 + 2*x + 1)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x^6 + x^5 + 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