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A315001
Coordination sequence Gal.6.190.4 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, 9, 15, 18, 23, 27, 31, 37, 40, 46, 50, 55, 61, 63, 69, 72, 77, 83, 85, 92, 95, 101, 107, 108, 115, 117, 123, 129, 130, 138, 140, 147, 153, 153, 161, 162, 169, 175, 175, 184, 185, 193, 199, 198, 207, 207, 215, 221, 220
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 18 2024: (Start)
a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - 2*a(n-8) + 2*a(n-9) - a(n-10) + a(n-11) - a(n-12) + a(n-13) - a(n-14) for n > 14.
G.f.: (x^2 + x + 1)*(x^12 + 3*x^11 + x^10 + 6*x^9 + x^8 + 7*x^7 + 7*x^5 + x^4 + 6*x^3 + x^2 + 3*x + 1)/((x - 1)^2*(x^4 - x^3 + x^2 - x + 1)*(x^4 + x^3 + x^2 + x + 1)^2). (End)
CROSSREFS
Sequence in context: A323197 A314999 A315000 * A315002 A315003 A315004
KEYWORD
nonn
AUTHOR
STATUS
approved