A310040 - OEIS

A310040

Coordination sequence Gal.6.109.1 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, 5, 9, 14, 21, 23, 21, 22, 27, 33, 39, 46, 51, 49, 45, 46, 51, 59, 69, 78, 81, 75, 69, 70, 75, 85, 99, 110, 111, 101, 93, 94, 99, 111, 129, 142, 141, 127, 117, 118, 123, 137, 159, 174, 171, 153, 141, 142, 147

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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 24 2019: (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 - 4*x^12 + 12*x^11 - 2*x^10 + 13*x^9 - x^8 + 10*x^7 + x^6 + 9*x^5 + 4*x^4 + 4*x^3 + 2*x^2 + x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^4 + 1)^2). (End)

CROSSREFS

Sequence in context: A054066 A081946 A166709 * A215369 A053618 A268345

Adjacent sequences: A310037 A310038 A310039 * A310041 A310042 A310043

KEYWORD

nonn

AUTHOR

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

STATUS

approved