A310039 Coordination sequence Gal.3.7.1 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.

1, 3, 5, 9, 12, 15, 17, 19, 24, 29, 31, 33, 36, 39, 41, 45, 50, 51, 51, 55, 62, 65, 65, 69, 74, 75, 75, 81, 88, 87, 85, 91, 100, 101, 99, 105, 112, 111, 109, 117, 126, 123, 119, 127, 138, 137, 133, 141, 150, 147

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

Table of n, a(n) for n=0..49.

Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers

Formula

Conjectures from Chai Wah Wu, Dec 24 2019: (Start)

a(n) = 3*a(n-1) - 5*a(n-2) + 6*a(n-3) - 5*a(n-4) + 3*a(n-5) - 2*a(n-6) + 3*a(n-7) - 5*a(n-8) + 6*a(n-9) - 5*a(n-10) + 3*a(n-11) - a(n-12) for n > 14.

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

Crossrefs

Sequence in context: A020946 A352596 A304525 * A091785 A191403 A233779

Adjacent sequences: A310036 A310037 A310038 * A310040 A310041 A310042

Keyword

nonn

Author

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

Status

approved