A313782 Coordination sequence Gal.5.289.1 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, 15, 21, 26, 31, 37, 42, 47, 52, 57, 62, 67, 73, 78, 83, 89, 94, 99, 104, 109, 114, 119, 125, 130, 135, 141, 146, 151, 156, 161, 166, 171, 177, 182, 187, 193, 198, 203, 208, 213, 218, 223, 229, 234, 239, 245, 250, 255

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, May 06 2025: (Start)

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

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

Conjecture: a(n) ~ 26*n/5. - Stefano Spezia, May 06 2025

Crossrefs

Sequence in context: A313780 A313781 A115181 * A313783 A313784 A313785

Adjacent sequences: A313779 A313780 A313781 * A313783 A313784 A313785

Keyword

nonn

Author

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

Status

approved