A314236 Coordination sequence Gal.6.626.1 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, 5, 11, 17, 23, 28, 33, 38, 43, 49, 55, 61, 66, 71, 77, 83, 89, 94, 99, 104, 109, 115, 121, 127, 132, 137, 143, 149, 155, 160, 165, 170, 175, 181, 187, 193, 198, 203, 209, 215, 221, 226, 231, 236, 241, 247, 253, 259, 264, 269

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, Apr 15 2024: (Start)

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

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

Crossrefs

Sequence in context: A314233 A314234 A314235 * A314237 A301718 A314238

Adjacent sequences: A314233 A314234 A314235 * A314237 A314238 A314239

Keyword

nonn,changed

Author

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

Status

approved