A315431 Coordination sequence Gal.6.669.6 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, 6, 11, 15, 22, 28, 33, 39, 44, 52, 56, 61, 64, 74, 78, 83, 88, 98, 100, 105, 110, 120, 120, 129, 132, 142, 142, 153, 154, 164, 166, 175, 174, 186, 188, 197, 196, 212, 210, 219, 218, 234, 230, 241, 242, 256, 252, 265, 264, 278

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

From Chai Wah Wu, Dec 20 2019: (Start)

a(n) = a(n-4) - a(n-5) + a(n-7) + a(n-9) - a(n-11) + a(n-12) - a(n-16) for n > 22 (conjectured).

G.f.: (-x^22 - x^17 + x^16 + 8*x^15 + 11*x^14 + 16*x^13 + 21*x^12 + 23*x^11 + 30*x^10 + 34*x^9 + 31*x^8 + 34*x^7 + 28*x^6 + 23*x^5 + 21*x^4 + 15*x^3 + 11*x^2 + 6*x + 1)/(x^16 - x^12 + x^11 - x^9 - x^7 + x^5 - x^4 + 1) (conjectured). (End)

Crossrefs

Sequence in context: A315428 A315429 A315430 * A315432 A315433 A315434

Adjacent sequences: A315428 A315429 A315430 * A315432 A315433 A315434

Keyword

nonn

Author

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

Status

approved