

A032086


Number of reversible strings with n beads of 3 colors. If more than 1 bead, not palindromic.


5



3, 3, 9, 36, 108, 351, 1053, 3240, 9720, 29403, 88209, 265356, 796068, 2390391, 7171173, 21520080, 64560240, 193700403, 581101209, 1743362676, 5230088028, 15690441231, 47071323693, 141214502520, 423643507560
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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 3, 0, 0, 0, ...
Conjectures from Colin Barker, Apr 02 2012: (Start)
a(n) = 3*a(n1) + 3*a(n2)  9*a(n3) for n > 4.
G.f.: 3*x*(1  2*x  3*x^2 + 9*x^3)/((1  3*x)*(1  3*x^2)).
(End)
Conjectures from Colin Barker, Mar 09 2017: (Start)
a(n) = (2*3^n  2*3^(n/2)) / 4 for n > 2 and even.
a(n) = (2*3^n  2*3^((n+1)/2)) / 4 for n > 2 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) = (3^n  3^(ceiling(n/2)) / 2 = (A000244(n)  A056449(n)) / 2 for n>1.  Robert A. Russell and Danny Rorabaugh, Jun 22 2018


MATHEMATICA

Join[{3}, LinearRecurrence[{3, 3, 9}, {3, 9, 36}, 24]] (* JeanFrançois Alcover, Oct 11 2017 *)


PROG

(PARI) a(n) = if(n<2, [3][n], (3^n  3^(ceil(n/2)))/2); \\ Andrew Howroyd, Oct 10 2017


CROSSREFS

Column 3 of A293500 for n>1.
Cf. A032120.
Sequence in context: A264412 A202889 A257620 * A241278 A100239 A245023
Adjacent sequences: A032083 A032084 A032085 * A032087 A032088 A032089


KEYWORD

nonn


AUTHOR

Christian G. Bower


STATUS

approved



