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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A291048 Number of nonequivalent maximal irredundant sets in the n-cycle graph up to rotation. 2
0, 1, 1, 2, 2, 3, 2, 3, 4, 8, 6, 11, 11, 17, 25, 32, 41, 59, 79, 118, 157, 221, 303, 436, 610, 864, 1215, 1724, 2436, 3484, 4926, 7029, 9990, 14270, 20354, 29113, 41572, 59517, 85186, 122127, 175018, 251176, 360404, 517758, 743895, 1069633, 1538313, 2213894 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Equivalently, the number of n-bead binary necklaces (with turnover not allowed) avoiding the patterns 111, 1101, 1011, 00000, 000010, 010000, 000100, 001000, 0100010.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Cycle Graph

Eric Weisstein's World of Mathematics, Irredundant Set

FORMULA

a(n) = (1/n) * Sum_{d|n} phi(n/d) * A286954(d).

EXAMPLE

Case n=7: admissible nonequivalent words are 0010011 and 0010101, so a(7)=2.

MATHEMATICA

Table[(1/n) Sum[EulerPhi[n/d] SeriesCoefficient[x^2*(2 + 3 x + 4 x^2 + 5 x^3 - 7 x^5 - 16 x^6 - 9 x^7 + 20 x^8 + 11 x^9 - 14 x^12)/(1 - x^2 - x^3 - x^4 - x^5 + x^7 + 2 x^8 + x^9 - 2 x^10 - x^11 + x^14), {x, 0, d}], {d, Divisors@ n}], {n, 48}] (* Michael De Vlieger, Aug 17 2017 *)

PROG

(PARI)

{my (v=concat([0], Vec((2 + 3*x + 4*x^2 + 5*x^3 - 7*x^5 - 16*x^6 - 9*x^7 + 20*x^8 + 11*x^9 - 14*x^12)/(1 - x^2 - x^3 - x^4 - x^5 + x^7 + 2*x^8 + x^9 - 2*x^10 - x^11 + x^14) + O(x^50))));

vector(length(v), n, sumdiv(n, d, eulerphi(n/d)*v[d])/n)}

CROSSREFS

Cf. A286954.

Sequence in context: A059896 A079542 A220370 * A022467 A169614 A037126

Adjacent sequences:  A291045 A291046 A291047 * A291049 A291050 A291051

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Aug 16 2017

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 20 22:22 EDT 2019. Contains 322310 sequences. (Running on oeis4.)