login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A031367 Inflation orbit counts. 6
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

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).

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-Fran├žois Alcover, Jul 09 2018 *)

CROSSREFS

Cf. A001350, A006206.

Sequence in context: A101506 A092434 A239632 * A073443 A257494 A302347

Adjacent sequences:  A031364 A031365 A031366 * A031368 A031369 A031370

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 12 19:19 EST 2018. Contains 317116 sequences. (Running on oeis4.)