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A314259
Coordination sequence Gal.3.60.1 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, 5, 11, 18, 22, 28, 34, 40, 45, 49, 57, 62, 67, 73, 79, 86, 89, 95, 102, 107, 112, 117, 125, 130, 134, 140, 147, 153, 156, 163, 170, 175, 179, 184, 193, 197, 201, 208, 215, 221, 223, 230, 238, 242, 246, 252, 261, 265, 268, 275
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, Apr 13 2024: (Start)
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - 3*a(n-6) + 4*a(n-7) - 3*a(n-8) + 2*a(n-9) - 2*a(n-10) + 2*a(n-11) - 2*a(n-12) + 2*a(n-13) - a(n-14) for n > 14.
G.f.: (x^2 + x + 1)*(x^12 + 2*x^11 + 2*x^9 - 2*x^8 + 6*x^7 - 3*x^6 + 6*x^5 - 2*x^4 + 2*x^3 + 2*x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^4 + 1)*(x^4 - x^2 + 1)). (End)
CROSSREFS
Sequence in context: A314256 A314257 A314258 * A166039 A314260 A314261
KEYWORD
nonn
AUTHOR
STATUS
approved