A310289 Coordination sequence Gal.4.19.1 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, 3, 8, 13, 14, 19, 26, 29, 34, 37, 41, 48, 51, 53, 58, 65, 67, 70, 77, 79, 84, 89, 91, 98, 101, 103, 110, 115, 117, 120, 127, 131, 134, 139, 141, 148, 153, 153, 160, 165, 167, 172, 177, 181, 184, 189, 193, 198, 203, 203

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 30 2026: (Start)

a(n) = - a(n-2) + a(n-3) + 2*a(n-5) + a(n-7) - a(n-8) - a(n-10) for n > 16.

G.f.: (-x^16 - x^15 - 2*x^14 - 2*x^13 + x^11 + 4*x^10 + 7*x^9 + 13*x^8 + 17*x^7 + 21*x^6 + 22*x^5 + 19*x^4 + 15*x^3 + 9*x^2 + 3*x + 1)/(x^10 + x^8 - x^7 - 2*x^5 - x^3 + x^2 + 1). (End)

Crossrefs

Sequence in context: A310286 A310287 A310288 * A310290 A043361 A023734

Adjacent sequences: A310286 A310287 A310288 * A310290 A310291 A310292

Keyword

nonn

Author

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

Status

approved