The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 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. 5
 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 a(n) = (5^n - 5^(ceiling(n/2)) / 2 = (A000351(n) - A056451(n)) / 2 for n>1. - Robert A. Russell and Danny Rorabaugh, Jun 22 2018 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 for n>1. Cf. A032122. Equals (A000351 - A056451) / 2 for n>1. Sequence in context: A003587 A268100 A205884 * A081076 A174462 A277247 Adjacent sequences:  A032085 A032086 A032087 * A032089 A032090 A032091 KEYWORD nonn AUTHOR 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.

Last modified June 14 05:10 EDT 2021. Contains 345018 sequences. (Running on oeis4.)