A310050 Coordination sequence Gal.4.36.1 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, 6, 10, 13, 16, 19, 20, 26, 35, 34, 31, 34, 46, 51, 46, 49, 56, 62, 61, 62, 69, 72, 76, 79, 82, 83, 84, 92, 99, 100, 97, 100, 110, 115, 112, 113, 122, 128, 127, 126, 133, 138, 140, 145, 148, 149, 148, 156, 165

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 24 2019: (Start)

a(n) = - a(n-2) + a(n-5) + 2*a(n-7) + a(n-9) - a(n-12) - a(n-14) for n > 16.

G.f.: (-2*x^16 + x^14 + 3*x^13 + 7*x^12 + 15*x^11 + 21*x^10 + 29*x^9 + 29*x^8 + 28*x^7 + 29*x^6 + 25*x^5 + 19*x^4 + 13*x^3 + 7*x^2 + 3*x + 1)/(x^14 + x^12 - x^9 - 2*x^7 - x^5 + x^2 + 1). (End)

Crossrefs

Sequence in context: A099822 A117549 A190767 * A356469 A028433 A310051

Adjacent sequences: A310047 A310048 A310049 * A310051 A310052 A310053

Keyword

nonn

Author

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

Status

approved