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A310019
Coordination sequence Gal.6.110.1 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, 10, 17, 21, 20, 19, 23, 34, 45, 45, 38, 39, 45, 52, 63, 71, 68, 59, 59, 72, 87, 91, 88, 87, 85, 88, 101, 113, 114, 109, 107, 112, 123, 129, 130, 133, 135, 136, 141, 149, 152, 151, 153, 162, 171, 169, 166, 171
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) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) + 2*a(n-7) - a(n-8) + 2*a(n-9) - 2*a(n-10) + 2*a(n-11) - 2*a(n-12) + a(n-13) - a(n-14) for n > 16.
G.f.: (-2*x^16 + 2*x^15 - x^14 + 4*x^13 + 4*x^12 + 11*x^11 + 15*x^10 + 18*x^9 + 16*x^8 + 18*x^7 + 18*x^6 + 18*x^5 + 13*x^4 + 9*x^3 + 4*x^2 + 2*x + 1)/((x - 1)^2*(x^2 + 1)*(x^2 - x + 1)*(x^2 + x + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). (End)
CROSSREFS
Sequence in context: A329467 A293818 A037246 * A261998 A270413 A270415
KEYWORD
nonn
AUTHOR
STATUS
approved