A315964 Coordination sequence Gal.6.528.6 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, 6, 9, 13, 18, 21, 26, 29, 36, 41, 43, 48, 53, 56, 61, 64, 72, 76, 77, 83, 88, 91, 96, 99, 108, 111, 111, 118, 123, 126, 131, 134, 144, 146, 145, 153, 158, 161, 166, 169, 180, 181, 179, 188, 193, 196, 201, 204, 216, 216

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

From Chai Wah Wu, Dec 20 2019: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7) + a(n-8) - a(n-9) + a(n-10) - a(n-11) + a(n-12) - a(n-13) + a(n-14) - a(n-15) for n > 15.

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

Crossrefs

Sequence in context: A171575 A186524 A315963 * A315965 A167614 A020751

Adjacent sequences: A315961 A315962 A315963 * A315965 A315966 A315967

Keyword

nonn

Author

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

Status

approved