A313921 Coordination sequence Gal.5.313.2 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, 5, 10, 16, 22, 27, 34, 41, 46, 52, 56, 59, 66, 73, 78, 84, 90, 95, 102, 109, 112, 116, 122, 127, 134, 141, 146, 152, 158, 163, 168, 173, 178, 184, 190, 195, 202, 209, 214, 220, 224, 227, 234, 241, 246, 252, 258, 263, 270, 277

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, Feb 09 2023: (Start)

a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 6*a(n-6) + 6*a(n-7) - 6*a(n-8) + 6*a(n-9) - 5*a(n-10) + 4*a(n-11) - 3*a(n-12) + 2*a(n-13) - a(n-14) for n > 14.

G.f.: (x^14 + 3*x^13 + 3*x^12 + 7*x^11 + 5*x^10 + 10*x^9 + 8*x^8 + 10*x^7 + 8*x^6 + 10*x^5 + 5*x^4 + 7*x^3 + 3*x^2 + 3*x + 1)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Sequence in context: A313918 A313919 A313920 * A313922 A313923 A313924

Adjacent sequences: A313918 A313919 A313920 * A313922 A313923 A313924

Keyword

nonn

Author

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

Status

approved