A029700 Number of words of length 6 in the n(n-1)/2 transpositions of S[ n ] equivalent to the identity.

0, 1, 243, 3936, 20860, 72315, 197421, 460768, 961416, 1843245, 3306655, 5621616, 9142068, 14321671, 21730905, 32075520, 46216336, 65190393, 90233451, 122803840, 164607660, 217625331, 284139493, 366764256, 468475800, 592644325, 743067351, 924004368

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = n*(n-1)*(15*n^4 + 30*n^3 - 105*n^2 - 700*n + 1344)/8.

G.f.: -x^2*(481*x^4 - 1624*x^3 + 2256*x^2 + 236*x + 1) / (x-1)^7. - Colin Barker, May 28 2015

Mathematica

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 243, 3936, 20860, 72315, 197421}, 30] (* Harvey P. Dale, Mar 27 2022 *)

Prog

(Magma) [n*(n-1)*(15*n^4+30*n^3-105*n^2-700*n+1344)/8: n in [1..45]]; // Vincenzo Librandi, Jun 30 2011
(PARI) concat(0, Vec(-x^2*(481*x^4-1624*x^3+2256*x^2+236*x+1) / (x-1)^7 + O(x^100))) \\ Colin Barker, May 28 2015

Crossrefs

Sequence in context: A226777 A016757 A133550 * A224003 A232027 A183808

Adjacent sequences: A029697 A029698 A029699 * A029701 A029702 A029703

Keyword

nonn,easy

Author

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

Extensions

a(1) corrected by Vincenzo Librandi, Jun 30 2011

Status

approved