A310640 Coordination sequence Gal.6.527.2 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, 4, 6, 14, 17, 21, 28, 28, 36, 36, 44, 47, 51, 58, 58, 66, 66, 74, 77, 81, 88, 88, 96, 96, 104, 107, 111, 118, 118, 126, 126, 134, 137, 141, 148, 148, 156, 156, 164, 167, 171, 178, 178, 186, 186, 194, 197, 201, 208, 208

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.

Conjectures: for k >= 1, a(7*k-1) = a(7*k) = 28 + (k-1)*30 and a(7*k+1) = a(7*k+2) = 36 + (k-1)*30. - Bernard Schott, Dec 24 2019

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 24 2019: (Start)

a(n) = a(n-1) + a(n-7) - a(n-8) for n > 9.

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

Crossrefs

Sequence in context: A310637 A310638 A310639 * A310641 A024461 A063811

Adjacent sequences: A310637 A310638 A310639 * A310641 A310642 A310643

Keyword

nonn

Author

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

Status

approved