A312508 - OEIS

%I #6 Oct 21 2023 15:10:42

%S 1,4,8,14,18,22,30,30,36,42,44,56,46,64,66,64,74,82,76,90,90,98,96,

%T 112,102,118,120,120,126,142,124,152,142,148,156,168,152,176,174,176,

%U 176,204,174,206,200,202,210,224,202,238

%N Coordination sequence Gal.5.250.2 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_, Jan 28 2020: (Start)

%F a(n) = - 3*a(n-1) - 6*a(n-2) - 9*a(n-3) - 11*a(n-4) - 11*a(n-5) - 8*a(n-6) - 2*a(n-7) + 6*a(n-8) + 14*a(n-9) + 20*a(n-10) + 22*a(n-11) + 20*a(n-12) + 14*a(n-13) + 6*a(n-14) - 2*a(n-15) - 8*a(n-16) - 11*a(n-17) - 11*a(n-18) - 9*a(n-19) - 6*a(n-20) - 3*a(n-21) - a(n-22) for n > 23.

%F G.f.: (-2*x^23 - 3*x^22 - x^21 + 16*x^20 + 63*x^19 + 151*x^18 + 295*x^17 + 488*x^16 + 718*x^15 + 954*x^14 + 1158*x^13 + 1294*x^12 + 1338*x^11 + 1276*x^10 + 1130*x^9 + 922*x^8 + 690*x^7 + 470*x^6 + 287*x^5 + 155*x^4 + 71*x^3 + 26*x^2 + 7*x + 1)/((x - 1)^2*(x + 1)^2*(x^2 + 1)*(x^2 - x + 1)*(x^2 + x + 1)^2*(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