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A311416 Coordination sequence Gal.4.48.1 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, 4, 8, 12, 17, 21, 24, 29, 35, 40, 43, 45, 49, 54, 58, 62, 67, 73, 78, 81, 84, 87, 90, 95, 101, 106, 110, 114, 119, 123, 125, 128, 133, 139, 144, 147, 151, 156, 160, 164, 168, 172, 176, 180, 185, 189, 192, 197, 203, 208 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
FORMULA
Conjectures from Chai Wah Wu, Mar 05 2024: (Start)
a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 7*a(n-6) + 8*a(n-7) - 8*a(n-8) + 8*a(n-9) - 7*a(n-10) + 6*a(n-11) - 5*a(n-12) + 4*a(n-13) - 3*a(n-14) + 2*a(n-15) - a(n-16) for n > 16.
G.f.: (x^16 + 2*x^15 + 3*x^14 + 4*x^13 + 6*x^12 + 5*x^11 + 8*x^10 + 8*x^9 + 10*x^8 + 8*x^7 + 8*x^6 + 5*x^5 + 6*x^4 + 4*x^3 + 3*x^2 + 2*x + 1)/((x - 1)^2*(x^2 + 1)*(x^4 + 1)*(x^4 - x^3 + x^2 - x + 1)*(x^4 + x^3 + x^2 + x + 1)). (End)
Conjecture: a(n) ~ 21*n/5. - Stefano Spezia, Mar 05 2024 after Chai Wah Wu
CROSSREFS
Sequence in context: A311413 A311414 A311415 * A311417 A311418 A311419
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)