A314658 Coordination sequence Gal.5.14.3 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, 9, 13, 15, 22, 26, 34, 36, 41, 41, 49, 53, 62, 63, 68, 67, 76, 80, 90, 90, 95, 93, 103, 107, 118, 117, 122, 119, 130, 134, 146, 144, 149, 145, 157, 161, 174, 171, 176, 171, 184, 188, 202, 198, 203, 197, 211, 215, 230

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, Jul 30 2022: (Start)

a(n) = a(n-1) - a(n-3) + a(n-4) + a(n-6) - a(n-7) + a(n-9) - a(n-10) for n > 13.

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

Crossrefs

Sequence in context: A314656 A098991 A314657 * A116616 A314659 A314660

Adjacent sequences: A314655 A314656 A314657 * A314659 A314660 A314661

Keyword

nonn

Author

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

Status

approved