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A032122 Number of reversible strings with n beads of 5 colors. 7
5, 15, 75, 325, 1625, 7875, 39375, 195625, 978125, 4884375, 24421875, 122078125, 610390625, 3051796875, 15258984375, 76294140625, 381470703125, 1907349609375, 9536748046875, 47683720703125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..500

C. G. Bower, Transforms (2)

Index entries for linear recurrences with constant coefficients, signature (5,5,-25).

FORMULA

"BIK" (reversible, indistinct, unlabeled) transform of 5, 0, 0, 0...

a(n) = 1/2 * (5^n + 5^floor((n+1)/2)) = 5*A001447(n+1). - Ralf Stephan, Jul 07 2003

G.f.: x*(5-10*x-25*x^2)/(1-5*x-5*x^2+25*x^3). - Colin Barker, Jan 30 2012

a(n) = 5*a(n-1) + 5*a(n-2) - 25*a(n-3). - Vincenzo Librandi, Jan 31 2012

MATHEMATICA

LinearRecurrence[{5, 5, -25}, {5, 15, 75}, 30] (* Vincenzo Librandi, Jan 31 2012 *)

k=5; Table[(k^n+k^Ceiling[n/2])/2, {n, 1, 30}] (*Robert A. Russell, Nov 25 2017*)

PROG

(MAGMA) I:=[5, 15, 75]; [n le 3 select I[n] else 5*Self(n-1)+ 5*Self(n-2)-25*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jan 31 2012

(PARI) a(n)=(5^((n+1)\2)+5^n)/2 \\ Charles R Greathouse IV, Jan 31 2012

CROSSREFS

Column 5 of A277504.

(A000351 + A056451) / 2.

Sequence in context: A149653 A149654 A149655 * A220818 A064678 A088935

Adjacent sequences:  A032119 A032120 A032121 * A032123 A032124 A032125

KEYWORD

nonn,easy

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified October 19 05:08 EDT 2018. Contains 316336 sequences. (Running on oeis4.)