A313571 Coordination sequence Gal.5.169.3 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, 10, 14, 19, 24, 29, 35, 39, 46, 48, 52, 60, 62, 71, 72, 82, 81, 85, 96, 95, 107, 105, 118, 114, 118, 132, 128, 143, 138, 154, 147, 151, 168, 161, 179, 171, 190, 180, 184, 204, 194, 215, 204, 226, 213, 217, 240, 227, 251

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 16 2026: (Start)

a(n) = 2*a(n-7) - a(n-14) for n > 17.

G.f.: (-x^17 - x^15 + 2*x^14 + 4*x^13 + 12*x^12 + 14*x^11 + 20*x^10 + 26*x^9 + 29*x^8 + 33*x^7 + 29*x^6 + 24*x^5 + 19*x^4 + 14*x^3 + 10*x^2 + 5*x + 1)/(x^14 - 2*x^7 + 1). (End)

Crossrefs

Sequence in context: A313568 A313569 A313570 * A313572 A313573 A313574

Adjacent sequences: A313568 A313569 A313570 * A313572 A313573 A313574

Keyword

nonn,more

Author

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

Status

approved