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A310031
Coordination sequence Gal.5.39.1 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, 3, 5, 8, 12, 16, 19, 20, 21, 24, 28, 32, 36, 39, 40, 41, 44, 49, 55, 58, 57, 57, 60, 65, 71, 75, 76, 76, 77, 81, 88, 94, 95, 93, 93, 97, 104, 110, 112, 112, 112, 114, 120, 127, 131, 131, 129, 130, 136, 143
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, Dec 10 2018: (Start)
a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) + a(n-13) - a(n-14) + a(n-15) - a(n-16) + a(n-17) - a(n-18) for n > 18.
G.f.: (x^18 + 2*x^17 + 3*x^16 + 5*x^15 + 7*x^14 + 9*x^13 + 9*x^12 + 8*x^11 + 8*x^10 + 8*x^9 + 8*x^8 + 8*x^7 + 9*x^6 + 9*x^5 + 7*x^4 + 5*x^3 + 3*x^2 + 2*x + 1)/(x^18 - x^17 + x^16 - x^15 + x^14 - x^13 - x^5 + x^4 - x^3 + x^2 - x + 1). (End)
CROSSREFS
Sequence in context: A045716 A236203 A122539 * A310032 A310033 A289073
KEYWORD
nonn
AUTHOR
STATUS
approved