A314159 Coordination sequence Gal.6.624.3 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, 11, 16, 22, 28, 33, 38, 44, 50, 55, 61, 66, 71, 77, 82, 88, 94, 99, 104, 110, 116, 121, 127, 132, 137, 143, 148, 154, 160, 165, 170, 176, 182, 187, 193, 198, 203, 209, 214, 220, 226, 231, 236, 242, 248, 253, 259, 264, 269

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 Colin Barker, Aug 27 2019: (Start)

G.f.: (1 + 3*x + 3*x^2 + 2*x^3 + 4*x^4 + 2*x^5 + 3*x^6 + 2*x^7 + 4*x^8 + 2*x^9 + 3*x^10 + 3*x^11 + x^12) / ((1 - x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)).

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - 2*a(n-8) + 2*a(n-9) - 2*a(n-10) + 2*a(n-11) - a(n-12) for n>12.

(End)

Crossrefs

Sequence in context: A314156 A314157 A314158 * A314160 A314161 A314162

Adjacent sequences: A314156 A314157 A314158 * A314160 A314161 A314162

Keyword

nonn

Author

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

Status

approved