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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A032088 Number of reversible strings with n beads of 5 colors. If more than 1 bead, not palindromic. 3
5, 10, 50, 300, 1500, 7750, 38750, 195000, 975000, 4881250, 24406250, 122062500, 610312500, 3051718750, 15258593750, 76293750000, 381468750000, 1907347656250, 9536738281250, 47683710937500 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

C. G. Bower, Transforms (2)

FORMULA

"BHK" (reversible, identity, unlabeled) transform of 5, 0, 0, 0...

Conjectures from Colin Barker, Jul 07 2012: (Start)

a(n) = 5*a(n-1) + 5*a(n-2) - 25*a(n-3) for n > 4.

G.f.: 5*x*(1 - 3*x - 5*x^2 + 25*x^3)/((1 - 5*x)*(1 - 5*x^2)).

(End)

Conjectures from Colin Barker, Mar 09 2017: (Start)

a(n) = 5^(n/2)*(5^(n/2) - 1) / 2 for n > 1 and even.

a(n) = -5*(5^(n/2-1/2) - 5^(n-1)) / 2 for n > 1 and odd.

(End)

The above conjectures are true: The second set follows from the definition and the first set can be derived from that. - Andrew Howroyd, Oct 10 2017

MATHEMATICA

Join[{5}, LinearRecurrence[{5, 5, -25}, {10, 50, 300}, 19]] (* Jean-François Alcover, Oct 11 2017 *)

PROG

(PARI) a(n) = if(n<2, [5][n], (5^n - 5^(ceil(n/2)))/2); \\ Andrew Howroyd, Oct 10 2017

CROSSREFS

Column 5 of A293500.

Cf. A032122.

Sequence in context: A003587 A268100 A205884 * A081076 A174462 A277247

Adjacent sequences:  A032085 A032086 A032087 * A032089 A032090 A032091

KEYWORD

nonn

AUTHOR

Christian G. Bower

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 February 21 12:54 EST 2018. Contains 299411 sequences. (Running on oeis4.)