A312105 Coordination sequence Gal.4.87.1 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, 4, 8, 13, 18, 22, 27, 33, 36, 40, 44, 49, 53, 58, 67, 67, 71, 75, 80, 84, 89, 101, 98, 102, 106, 111, 115, 120, 135, 129, 133, 137, 142, 146, 151, 169, 160, 164, 168, 173, 177, 182, 203, 191, 195, 199, 204, 208, 213, 237

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 20 2022: (Start)

a(n) = 2*a(n-7) - a(n-14) for n > 16.

G.f.: (-x^16 - x^15 + 2*x^14 + 4*x^13 + 9*x^12 + 13*x^11 + 18*x^10 + 24*x^9 + 28*x^8 + 31*x^7 + 27*x^6 + 22*x^5 + 18*x^4 + 13*x^3 + 8*x^2 + 4*x + 1)/(x^14 - 2*x^7 + 1). (End)

Crossrefs

Sequence in context: A312102 A312103 A312104 * A312106 A312107 A312108

Adjacent sequences: A312102 A312103 A312104 * A312106 A312107 A312108

Keyword

nonn

Author

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

Status

approved