A315520 Coordination sequence Gal.4.140.3 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, 6, 11, 17, 22, 27, 33, 38, 44, 50, 55, 61, 66, 71, 77, 82, 88, 94, 99, 105, 110, 115, 121, 126, 132, 138, 143, 149, 154, 159, 165, 170, 176, 182, 187, 193, 198, 203, 209, 214, 220, 226, 231, 237, 242, 247, 253, 258, 264, 270

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, Jun 11 2020: (Start)

a(n) = 2*a(n-1) - a(n-2) - a(n-4) + 2*a(n-5) - a(n-6) for n > 6.

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

Conjecture: a(n) = (22*n + 2*A188510(n))/4 for n > 0. - Stefano Spezia, Jul 30 2022

Crossrefs

Cf. A188510, A250120.

Sequence in context: A001964 A315518 A315519 * A315521 A315522 A315523

Adjacent sequences: A315517 A315518 A315519 * A315521 A315522 A315523

Keyword

nonn

Author

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

Status

approved