A310018 Coordination sequence Gal.4.34.1 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, 3, 5, 10, 14, 17, 17, 20, 27, 33, 36, 40, 39, 39, 44, 55, 65, 64, 60, 61, 65, 72, 83, 91, 84, 82, 87, 93, 100, 109, 111, 106, 108, 115, 121, 126, 129, 133, 132, 136, 143, 147, 146, 151, 159, 160, 164, 169, 167, 168

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, Dec 10 2018: (Start)

a(n) = a(n-6) + a(n-7) - a(n-13) for n > 23.

G.f.: (-2*x^23 - 4*x^22 + 2*x^20 - 2*x^18 + 2*x^17 + 6*x^16 + 3*x^13 + 5*x^12 + 9*x^11 + 12*x^10 + 18*x^9 + 19*x^8 + 16*x^7 + 16*x^6 + 17*x^5 + 14*x^4 + 10*x^3 + 5*x^2 + 3*x + 1)/(x^13 - x^7 - x^6 + 1). (End)

Crossrefs

Sequence in context: A360956 A273160 A285138 * A048214 A195094 A308805

Adjacent sequences: A310015 A310016 A310017 * A310019 A310020 A310021

Keyword

nonn

Author

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

Status

approved