A310190 Coordination sequence Gal.5.19.2 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, 7, 10, 14, 20, 21, 27, 28, 31, 37, 38, 44, 50, 49, 57, 56, 59, 67, 66, 74, 80, 77, 87, 84, 87, 97, 94, 104, 110, 105, 117, 112, 115, 127, 122, 134, 140, 133, 147, 140, 143, 157, 150, 164, 170, 161, 177, 168, 171

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 24 2019: (Start)

a(n) = a(n-1) - a(n-4) + a(n-5) + a(n-8) - a(n-9) + a(n-12) - a(n-13) for n > 13.

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

Crossrefs

Sequence in context: A310189 A293788 A319480 * A307203 A347638 A224880

Adjacent sequences: A310187 A310188 A310189 * A310191 A310192 A310193

Keyword

nonn

Author

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

Status

approved