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 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. 0

%I #11 Oct 21 2023 15:10:34

%S 1,4,6,14,17,21,28,28,36,36,44,47,51,58,58,66,66,74,77,81,88,88,96,96,

%T 104,107,111,118,118,126,126,134,137,141,148,148,156,156,164,167,171,

%U 178,178,186,186,194,197,201,208,208

%N 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.

%C 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.

%C 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

%H Brian Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>

%F Conjectures from _Chai Wah Wu_, Dec 24 2019: (Start)

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

%F 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)

%K nonn

%O 0,2

%A _Brian Galebach_ and _N. J. A. Sloane_, Jun 18 2018

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Last modified December 9 20:47 EST 2023. Contains 367695 sequences. (Running on oeis4.)