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A032087 Number of reversible strings with n beads of 4 colors. If more than 1 bead, not palindromic. 3
4, 6, 24, 120, 480, 2016, 8064, 32640, 130560, 523776, 2095104, 8386560, 33546240, 134209536, 536838144, 2147450880, 8589803520, 34359607296, 137438429184, 549755289600, 2199021158400, 8796090925056, 35184363700224, 140737479966720, 562949919866880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

C. G. Bower, Transforms (2)

Elizabeth Wilmer, Notes on Stephan's conjectures 72, 73 and 74

Index entries for linear recurrences with constant coefficients, signature (4,4,-16).

FORMULA

"BHK" (reversible, identity, unlabeled) transform of 4, 0, 0, 0...

a(2*n+1) = 2^(4*n+1) - 2^(2*n+1), a(2*n) = 2^(4*n-1) - 2^(2*n) + 2^(2*n-1), a(1)=4.

From R. J. Mathar, Mar 20 2009: (Start)

a(n) = 4*a(n-1) + 4*a(n-2) - 16*a(n-3) for n > 4.

G.f.: 2*x*(-5*x+2-8*x^2+32*x^3) / ((2*x+1)*(2*x-1)*(4*x-1)).

(End)

From Colin Barker, Mar 08 2017: (Start)

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

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

(End)

MATHEMATICA

Join[{4}, LinearRecurrence[{4, 4, -16}, {6, 24, 120}, 24]] (* Jean-François Alcover, Oct 11 2017 *)

PROG

(PARI) Vec(2*x*(2 - 5*x - 8*x^2 + 32*x^3) / ((1 - 2*x)*(1 + 2*x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Mar 08 2017

CROSSREFS

Column 4 of A293500.

Cf. A088037.

Cf. A026337 (bisection), A032121.

Sequence in context: A067001 A057343 A000287 * A165164 A241602 A136591

Adjacent sequences:  A032084 A032085 A032086 * A032088 A032089 A032090

KEYWORD

nonn,easy

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified February 22 19:36 EST 2018. Contains 299469 sequences. (Running on oeis4.)