A310007 Coordination sequence Gal.4.31.1 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, 4, 7, 12, 18, 19, 17, 18, 23, 27, 32, 40, 43, 40, 37, 38, 43, 48, 57, 68, 68, 61, 57, 58, 63, 69, 82, 96, 93, 82, 77, 78, 83, 90, 107, 124, 118, 103, 97, 98, 103, 111, 132, 152, 143, 124, 117, 118, 123

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) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 7*a(n-6) + 8*a(n-7) - 7*a(n-8) + 6*a(n-9) - 5*a(n-10) + 4*a(n-11) - 3*a(n-12) + 2*a(n-13) - a(n-14) for n > 16.

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

Crossrefs

Sequence in context: A130324 A020677 A362222 * A158237 A117950 A025047

Adjacent sequences: A310004 A310005 A310006 * A310008 A310009 A310010

Keyword

nonn

Author

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

Status

approved