A029698 Number of words of length 2n in the 10 transpositions of S[5] equivalent to the identity.

10, 340, 20860, 1770940, 169271260, 16731772540, 1668294277660, 166707356798140, 16667683919380060, 1666692097982207740, 166667302449546018460, 16666682561238613761340, 1666667064030965197232860, 166666676600774129343618940, 16666666915019353231241663260

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Justin Meiners, Computing the Rank of Braids, Master's Thesis, Brigham Young University (2021) 8947.

Index entries for linear recurrences with constant coefficients, signature (129,-3000,10000).

Formula

a(n) = (25*4^n+16*25^n +100^n)/60.

a(n) = 129*a(n-1)-3000*a(n-2)+10000*a(3). - Colin Barker, May 28 2015

G.f.: -10*x*(700*x^2-95*x+1) / ((4*x-1)*(25*x-1)*(100*x-1)). - Colin Barker, May 28 2015

Mathematica

Rest@ CoefficientList[Series[-10 x (700 x^2 - 95 x + 1)/((4 x - 1)*(25 x - 1)*(100 x - 1)), {x, 0, 15}], x] (* Michael De Vlieger, Jul 06 2021 *)

Prog

(Magma) [(25*4^n+16*25^n +100^n)/60: n in [1..15]]; // Vincenzo Librandi, Jun 30 2011
(PARI) Vec(-10*x*(700*x^2-95*x+1) / ((4*x-1)*(25*x-1)*(100*x-1)) + O(x^100)) \\ Colin Barker, May 28 2015

Crossrefs

Sequence in context: A046747 A338799 A006426 * A197598 A197982 A217506

Adjacent sequences: A029695 A029696 A029697 * A029699 A029700 A029701

Keyword

nonn,easy

Author

Paolo Dominici (pl.dm(AT)libero.it)

Status

approved