A315540 Coordination sequence Gal.6.643.4 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, 17, 23, 29, 34, 39, 45, 51, 57, 62, 68, 74, 79, 85, 91, 97, 102, 107, 113, 119, 125, 130, 136, 142, 147, 153, 159, 165, 170, 175, 181, 187, 193, 198, 204, 210, 215, 221, 227, 233, 238, 243, 249, 255, 261, 266, 272, 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

Conjectures from Chai Wah Wu, Jan 21 2021: (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) - 2*a(n-10) + 2*a(n-11) - a(n-12) for n > 12.

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

Crossrefs

Sequence in context: A315537 A315538 A315539 * A315541 A315542 A315543

Adjacent sequences: A315537 A315538 A315539 * A315541 A315542 A315543

Keyword

nonn

Author

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

Status

approved