A314377 Coordination sequence Gal.6.109.6 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, 8, 10, 12, 14, 18, 25, 32, 35, 34, 34, 36, 38, 44, 55, 64, 65, 60, 58, 60, 62, 70, 85, 96, 95, 86, 82, 84, 86, 96, 115, 128, 125, 112, 106, 108, 110, 122, 145, 160, 155, 138, 130, 132, 134, 148, 175, 192, 185

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, Apr 10 2021: (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 > 14.

G.f.: (x^14 + 3*x^13 + x^12 + 5*x^11 + x^10 + 7*x^9 + 3*x^8 + 12*x^7 + 3*x^6 + 7*x^5 + x^4 + 5*x^3 + x^2 + 3*x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^4 + 1)^2). (End)

Crossrefs

Sequence in context: A173298 A248356 A115401 * A314378 A314379 A153663

Adjacent sequences: A314374 A314375 A314376 * A314378 A314379 A314380

Keyword

nonn

Author

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

Status

approved