A315628 Coordination sequence Gal.4.104.4 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, 12, 16, 18, 28, 34, 34, 44, 48, 54, 62, 64, 68, 76, 82, 88, 90, 98, 100, 110, 114, 118, 124, 130, 134, 144, 142, 152, 156, 164, 166, 174, 176, 184, 190, 198, 194, 208, 208, 218, 222, 228, 228, 240, 242, 252, 250, 262, 260

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, Jun 09 2022: (Start)

a(n) = a(n-6) + a(n-10) - a(n-16) for n > 21.

G.f.: (-2*x^21 - 2*x^20 + 2*x^18 + x^16 + 6*x^15 + 14*x^14 + 18*x^13 + 18*x^12 + 28*x^11 + 35*x^10 + 32*x^9 + 32*x^8 + 28*x^7 + 33*x^6 + 28*x^5 + 18*x^4 + 16*x^3 + 12*x^2 + 6*x + 1)/(x^16 - x^10 - x^6 + 1). (End)

Crossrefs

Sequence in context: A315625 A315626 A315627 * A349995 A315629 A315630

Adjacent sequences: A315625 A315626 A315627 * A315629 A315630 A315631

Keyword

nonn

Author

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

Status

approved