A310027 Coordination sequence Gal.5.41.2 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, 5, 8, 11, 14, 18, 21, 23, 25, 28, 32, 34, 35, 39, 44, 47, 48, 50, 55, 58, 58, 61, 66, 69, 71, 74, 78, 80, 81, 85, 89, 90, 92, 97, 102, 103, 103, 108, 113, 113, 114, 119, 124, 126, 127, 131, 135, 136, 138

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, Dec 10 2018: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-19) - a(n-20) + a(n-21) - a(n-22) for n > 22.

G.f.: (x + 1)^2*(x^2 - x + 1)^2*(x^2 + x + 1)*(x^14 + x^13 + x^12 + x^11 - x^10 + x^8 + x^7 + x^6 - x^4 + x^3 + x^2 + x + 1)/(x^22 - x^21 + x^20 - x^19 - x^3 + x^2 - x + 1). (End)

Crossrefs

Sequence in context: A278586 A001855 A006591 * A310028 A287414 A052488

Adjacent sequences: A310024 A310025 A310026 * A310028 A310029 A310030

Keyword

nonn

Author

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

Status

approved