A313297 Coordination sequence Gal.6.210.1 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, 4, 9, 15, 21, 27, 33, 39, 45, 51, 57, 62, 66, 70, 75, 81, 87, 93, 99, 105, 111, 117, 123, 128, 132, 136, 141, 147, 153, 159, 165, 171, 177, 183, 189, 194, 198, 202, 207, 213, 219, 225, 231, 237, 243, 249, 255, 260, 264, 268

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 22 2021: (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 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)/((x - 1)^2*(x^2 + 1)*(x^2 - x + 1)*(x^4 - x^2 + 1)). (End)

Crossrefs

Sequence in context: A313294 A313295 A313296 * A270545 A359626 A358243

Adjacent sequences: A313294 A313295 A313296 * A313298 A313299 A313300

Keyword

nonn

Author

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

Status

approved