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A032092 Number of reversible strings with n-1 beads of 2 colors. 5 beads are black. String is not palindromic. 4
3, 9, 28, 60, 126, 226, 396, 636, 1001, 1491, 2184, 3080, 4284, 5796, 7752, 10152, 13167, 16797, 21252, 26532, 32890, 40326, 49140, 59332, 71253, 84903, 100688, 118608, 139128, 162248, 188496, 217872, 250971, 287793, 329004, 374604, 425334, 481194, 543004 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,1

COMMENTS

If the offset is changed to 3, this is the 2nd Witt transform of A000217 [Moree]. - R. J. Mathar, Nov 08 2008

LINKS

Colin Barker, Table of n, a(n) for n = 7..1000

C. G. Bower, Transforms (2)

Pieter Moree, The formal series Witt transform, Discr. Math. no. 295 vol. 1-3 (2005) 143-160. - R. J. Mathar, Nov 08 2008

Index entries for linear recurrences with constant coefficients, signature (3,0,-8,6,6,-8,0,3,-1).

FORMULA

"BHK[ 6 ]" (reversible, identity, unlabeled, 6 parts) transform of 1, 1, 1, 1...

G.f.: x^7*(3+x^2)/((1-x)^6*(1+x)^3). - R. J. Mathar, Nov 08 2008

From Colin Barker, Mar 07 2015: (Start)

a(n) = (2*n^5-30*n^4+170*n^3-480*n^2+728*n-480)/480 if n is even.

a(n) = (2*n^5-30*n^4+170*n^3-450*n^2+548*n-240)/480 if n is odd.

(End)

MATHEMATICA

LinearRecurrence[{3, 0, -8, 6, 6, -8, 0, 3, -1}, {3, 9, 28, 60, 126, 226, 396, 636, 1001}, 50] (* Harvey P. Dale, Mar 19 2017 *)

PROG

(PARI) Vec(x^7*(3+x^2)/((1-x)^6*(1+x)^3) + O(x^100)) \\ Colin Barker, Mar 07 2015

CROSSREFS

Cf. A282011.

Sequence in context: A102558 A022767 A015638 * A026524 A282081 A022631

Adjacent sequences:  A032089 A032090 A032091 * A032093 A032094 A032095

KEYWORD

nonn,easy

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified February 19 13:20 EST 2018. Contains 299333 sequences. (Running on oeis4.)