A310936 Coordination sequence Gal.3.7.3 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, 4, 7, 8, 8, 10, 17, 24, 28, 28, 27, 28, 32, 40, 47, 48, 46, 48, 55, 60, 62, 64, 65, 64, 66, 76, 85, 84, 80, 84, 93, 96, 96, 100, 103, 100, 100, 112, 123, 120, 114, 120, 131, 132, 130, 136, 141, 136, 134, 148

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, Mar 11 2021: (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 > 17.

G.f.: (-2*x^17 + 2*x^16 - 2*x^15 + 2*x^14 + 3*x^12 - x^11 + 2*x^10 - 3*x^9 + 4*x^8 - x^7 + 4*x^6 + x^5 + x^3 + x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^2 - x + 1)*(x^4 - x^2 + 1)). (End)

Crossrefs

Sequence in context: A310937 A090383 A179620 * A333202 A082390 A011517

Adjacent sequences: A310933 A310934 A310935 * A310937 A310938 A310939

Keyword

nonn

Author

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

Status

approved