A315628 - OEIS

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

%S 1,6,12,16,18,28,34,34,44,48,54,62,64,68,76,82,88,90,98,100,110,114,

%T 118,124,130,134,144,142,152,156,164,166,174,176,184,190,198,194,208,

%U 208,218,222,228,228,240,242,252,250,262,260

%N Coordination sequence Gal.4.104.4 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 09 2022: (Start)

%F a(n) = a(n-6) + a(n-10) - a(n-16) for n > 21.

%F G.f.: (-2*x^21 - 2*x^20 + 2*x^18 + x^16 + 6*x^15 + 14*x^14 + 18*x^13 + 18*x^12 + 28*x^11 + 35*x^10 + 32*x^9 + 32*x^8 + 28*x^7 + 33*x^6 + 28*x^5 + 18*x^4 + 16*x^3 + 12*x^2 + 6*x + 1)/(x^16 - x^10 - x^6 + 1). (End)

%K nonn

%O 0,2

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