A310601 Coordination sequence Gal.6.32.6 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, 4, 6, 14, 14, 18, 20, 30, 28, 38, 36, 46, 44, 48, 50, 62, 58, 70, 66, 78, 74, 78, 80, 94, 88, 102, 96, 110, 104, 108, 110, 126, 118, 134, 126, 142, 134, 138, 140, 158, 148, 166, 156, 174, 164, 168, 170, 190, 178, 198

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, Nov 18 2025: (Start)

a(n) = 2*a(n-8) - a(n-16) for n > 17.

G.f.: (-2*x^17 + 3*x^16 + 2*x^15 + 10*x^14 + 12*x^13 + 16*x^12 + 18*x^11 + 24*x^10 + 30*x^9 + 26*x^8 + 30*x^7 + 20*x^6 + 18*x^5 + 14*x^4 + 14*x^3 + 6*x^2 + 4*x + 1)/(x^16 - 2*x^8 + 1). (End)

Crossrefs

Sequence in context: A349171 A338658 A344224 * A310602 A296910 A310603

Adjacent sequences: A310598 A310599 A310600 * A310602 A310603 A310604

Keyword

nonn

Author

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

Status

approved