A315129 Coordination sequence Gal.6.401.5 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, 10, 12, 18, 22, 30, 30, 38, 44, 50, 54, 54, 62, 66, 68, 74, 82, 88, 94, 98, 92, 106, 110, 106, 118, 126, 132, 138, 142, 130, 150, 154, 144, 162, 170, 176, 182, 186, 168, 194, 198, 182, 206, 214, 220, 226, 230, 206, 238

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 19 2025: (Start)

a(n) = 2*a(n-9) - a(n-18) for n > 21.

G.f.: (-4*x^21 + x^18 + 6*x^17 + 14*x^16 + 8*x^15 + 22*x^14 + 26*x^13 + 30*x^12 + 34*x^11 + 38*x^10 + 42*x^9 + 38*x^8 + 30*x^7 + 30*x^6 + 22*x^5 + 18*x^4 + 12*x^3 + 10*x^2 + 6*x + 1)/(x^18 - 2*x^9 + 1). (End)

Crossrefs

Sequence in context: A380983 A114520 A315128 * A315130 A315131 A046288

Adjacent sequences: A315126 A315127 A315128 * A315130 A315131 A315132

Keyword

nonn

Author

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

Status

approved