Coordination sequence Gal.6.609.6 where GGal.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.

proposed

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proposed

From Chai Wah Wu, Dec 20 2019: (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) - 7*a(n-8) + 6*a(n-9) - 5*a(n-10) + 4*a(n-11) - 3*a(n-12) + 2*a(n-13) - a(n-14) for n > 14 (conjectured).

G.f.: (x^14 + 4*x^13 + 3*x^12 + 5*x^11 + 5*x^10 + 6*x^9 + 7*x^8 + 13*x^7 + 7*x^6 + 6*x^5 + 5*x^4 + 5*x^3 + 3*x^2 + 4*x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^4 + 1)^2) (conjectured). (End)

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0,2

Brian Galebache, Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>

Coordination sequence Gal.6.609.6 where G.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.

1, 6, 12, 15, 18, 21, 24, 33, 42, 45, 48, 51, 54, 57, 60, 72, 84, 84, 84, 87, 90, 93, 96, 111, 126, 123, 120, 123, 126, 129, 132, 150, 168, 162, 156, 159, 162, 165, 168, 189, 210, 201, 192, 195, 198, 201, 204, 228, 252, 240

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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.

Brian Galebache, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>

nonn

Brian Galebach and N. J. A. Sloane, Jun 18 2018

approved