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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056488 Number of periodic palindromes using a maximum of six different symbols. 5
6, 21, 36, 126, 216, 756, 1296, 4536, 7776, 27216, 46656, 163296, 279936, 979776, 1679616, 5878656, 10077696, 35271936, 60466176, 211631616, 362797056, 1269789696, 2176782336, 7618738176, 13060694016, 45712429056, 78364164096, 274274574336, 470184984576 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also number of necklaces with n beads and 6 colors that are the same when turned over and hence have reflection symmetry. - Herbert Kociemba, Nov 24 2016

REFERENCES

M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,6).

FORMULA

a(n) = 6^((n+1)/2) for n odd, a(n) = 6^(n/2)*7/2 for n even.

From Colin Barker, Jul 08 2012: (Start)

a(n) = 6*a(n-2).

G.f.: 3*x*(2+7*x)/(1-6*x^2). (End)

a(n) = (k^floor((n+1)/2) + k^ceiling((n+1)/2)) / 2, where k = 6 is the number of possible colors. - Robert A. Russell, Sep 22 2018

EXAMPLE

G.f. = 6*x + 21*x^2 + 36*x^3 + 126*x^4 + 216*x^5 + 756*x^6 + 1296*x^7 + ...

For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome.

MATHEMATICA

LinearRecurrence[{0, 6}, {6, 21}, 30] (* Harvey P. Dale, Feb 02 2015 *)

k = 6; Table[(k^Floor[(n + 1)/2] + k^Ceiling[(n + 1)/2]) / 2, {n, 30}] (* Robert A. Russell, Sep 21 2018 *)

If[EvenQ[#], 6^(# / 2) 7/2, 6^((# + 1) / 2)]&/@Range[30] (* Vincenzo Librandi, Sep 22 2018 *)

PROG

(PARI) a(n) = if(n%2, 6^((n+1)/2), 7*6^(n/2)/2); \\ Altug Alkan, Sep 21 2018

(MAGMA) [IsEven(n) select 6^(n div 2)*7/2 else 6^((n+1) div 2): n in [1..30]]; // Vincenzo Librandi, Sep 22 2018

CROSSREFS

Column 6 of A284855.

Cf. A029744, A038754, A056452.

Sequence in context: A151943 A207339 A284988 * A031042 A064431 A031094

Adjacent sequences:  A056485 A056486 A056487 * A056489 A056490 A056491

KEYWORD

nonn,easy

AUTHOR

Marks R. Nester

EXTENSIONS

More terms from Vincenzo Librandi, Sep 22 2018

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 July 21 19:25 EDT 2019. Contains 325199 sequences. (Running on oeis4.)