login
A314400
Coordination sequence Gal.6.392.6 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.
0
1, 5, 8, 11, 20, 23, 26, 31, 36, 41, 42, 49, 56, 59, 60, 65, 74, 75, 78, 85, 92, 95, 94, 101, 110, 113, 112, 119, 130, 129, 128, 137, 148, 149, 146, 155, 166, 165, 162, 173, 186, 183, 180, 191, 202, 201, 198, 209, 222, 219
OFFSET
0,2
COMMENTS
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.
FORMULA
Conjectures from Chai Wah Wu, Jan 12 2023: (Start)
a(n) = - a(n-2) + a(n-3) + a(n-5) - a(n-6) + a(n-7) - a(n-8) + 2*a(n-9) - a(n-10) + a(n-11) - a(n-12) + a(n-13) + a(n-15) - a(n-16) - a(n-18) for n > 18.
G.f.: (x^18 + 5*x^17 + 9*x^16 + 15*x^15 + 23*x^14 + 25*x^13 + 31*x^12 + 30*x^11 + 32*x^10 + 32*x^9 + 32*x^8 + 30*x^7 + 31*x^6 + 25*x^5 + 23*x^4 + 15*x^3 + 9*x^2 + 5*x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^2 + x + 1)*(x^4 - x^2 + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). (End)
CROSSREFS
Sequence in context: A175319 A154486 A162612 * A314401 A355168 A237434
KEYWORD
nonn
AUTHOR
STATUS
approved