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 A031367 Inflation orbit counts. 8
 1, 0, 3, 4, 10, 12, 28, 40, 72, 110, 198, 300, 520, 812, 1350, 2160, 3570, 5688, 9348, 15000, 24444, 39402, 64078, 103320, 167750, 270920, 439128, 709800, 1149850, 1859010, 3010348, 4868640, 7880994, 12748470, 20633200, 33379200, 54018520, 87394452, 141421800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also number of primitive Lucas strings of length n [Ashrafi et al.] - N. J. A. Sloane, Nov 19 2014 The preceding comment is true for all n except n=2, as there are 2 primitive Lucas strings of length 2. The sequence of the number of primitive Lucas strings is the Möbius transform of the Lucas numbers A000032. - Pontus von Brömssen, Jan 24 2019 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..2000 A. R. Ashrafi, J. Azarija, K. Fathalikhani, S. Klavzar, et al., Orbits of Fibonacci and Lucas cubes, dihedral transformations, and asymmetric strings, 2014. A. R. Ashrafi, J. Azarija, K. Fathalikhani, S. Klavzar and M. Petkovsek, Vertex and edge orbits of Fibonacci and Lucas cubes, 2014; See Table 3. Michael Baake, Joachim Hermisson, Peter Pleasants, The torus parametrization of quasiperiodic LI-classes J. Phys. A 30 (1997), no. 9, 3029-3056. FORMULA If b(n) is the n-th term of A001350, then a(n) = Sum_{d|n} mu(d)b(n/d). a(n) = n * A060280(n). G.f.: Sum_{k>=1} mu(k) * x^k * (1 + x^(2*k)) / ((1 - x^(2*k)) * (1 - x^k - x^(2*k))). - Ilya Gutkovskiy, Feb 06 2020 MAPLE A031367 := proc(n)     add( numtheory[mobius](d)*A001350(n/d), d=numtheory[divisors](n)) ; end proc: # R. J. Mathar, Jul 15 2016 # second Maple program: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(binomial(a(i)/i+j-1, j)*b(n-i*j, i-1), j=0..n/i)))     end: a:= proc(n) a(n):= ((<<0|1>, <1|1>>^n)[1, 2]-b(n, n-1))*n end: seq(a(n), n=1..40);  # Alois P. Heinz, Jun 22 2018 MATHEMATICA a[n_] := n*Sum[MoebiusMu[d]*Sum[Binomial[k-1, 2k-n/d]/(n-d*k), {k, 0, n/d-1} ], {d, Divisors[n]}]; Array[a, 40] (* Jean-François Alcover, Jul 09 2018 *) CROSSREFS Cf. A001350, A006206, A000032. Sequence in context: A101506 A092434 A239632 * A073443 A257494 A302347 Adjacent sequences:  A031364 A031365 A031366 * A031368 A031369 A031370 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from James A. Sellers STATUS approved

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Last modified August 15 02:47 EDT 2022. Contains 356122 sequences. (Running on oeis4.)