A314929 Coordination sequence Gal.5.189.5 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, 9, 14, 20, 21, 30, 33, 35, 44, 46, 51, 58, 61, 63, 72, 74, 77, 90, 87, 91, 102, 100, 105, 118, 117, 117, 132, 128, 131, 148, 143, 147, 160, 156, 159, 176, 171, 173, 192, 182, 187, 206, 197, 201, 220, 212, 213, 236, 225

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, Jun 12 2026: (Start)

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

G.f.: (x^14 + 5*x^13 + 11*x^12 + 18*x^11 + 25*x^10 + 29*x^9 + 40*x^8 + 37*x^7 + 40*x^6 + 30*x^5 + 25*x^4 + 18*x^3 + 10*x^2 + 5*x + 1)/(x^14 + x^12 - x^11 + x^10 - x^9 - 2*x^7 - x^5 + x^4 - x^3 + x^2 + 1). (End)

Crossrefs

Sequence in context: A314927 A074375 A314928 * A314930 A314931 A314932

Adjacent sequences: A314926 A314927 A314928 * A314930 A314931 A314932

Keyword

nonn

Author

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

Status

approved