A314400 Coordination sequence Gal.6.392.6 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, 5, 8, 11, 20, 23, 26, 31, 36, 41, 42, 49, 56, 59, 60, 65, 74, 75, 78, 85, 92, 95, 94, 101, 110, 113, 112, 119, 130, 129, 128, 137, 148, 149, 146, 155, 166, 165, 162, 173, 186, 183, 180, 191, 202, 201, 198, 209, 222, 219

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, Jan 12 2023: (Start)

a(n) = - a(n-2) + a(n-3) + a(n-5) - a(n-6) + a(n-7) - a(n-8) + 2*a(n-9) - a(n-10) + a(n-11) - a(n-12) + a(n-13) + a(n-15) - a(n-16) - a(n-18) for n > 18.

G.f.: (x^18 + 5*x^17 + 9*x^16 + 15*x^15 + 23*x^14 + 25*x^13 + 31*x^12 + 30*x^11 + 32*x^10 + 32*x^9 + 32*x^8 + 30*x^7 + 31*x^6 + 25*x^5 + 23*x^4 + 15*x^3 + 9*x^2 + 5*x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^2 + x + 1)*(x^4 - x^2 + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Sequence in context: A175319 A154486 A162612 * A314401 A355168 A237434

Adjacent sequences: A314397 A314398 A314399 * A314401 A314402 A314403

Keyword

nonn

Author

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

Status

approved