A029699 Number of words of length 4 in the n(n-1)/2 transpositions of S[ n ] equivalent to the identity.

0, 1, 27, 120, 340, 765, 1491, 2632, 4320, 6705, 9955, 14256, 19812, 26845, 35595, 46320, 59296, 74817, 93195, 114760, 139860, 168861, 202147, 240120, 283200, 331825, 386451, 447552, 515620, 591165, 674715, 766816, 868032, 978945, 1100155, 1232280, 1375956

Offset

1,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = n*(n-1)*(3*n^2+n-12)/4.

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>5. - Colin Barker, May 28 2015

G.f.: x^2*(5*x^2-22*x-1) / (x-1)^5. - Colin Barker, May 28 2015

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 27, 120, 340}, 50] (* Harvey P. Dale, Jan 10 2022 *)

Prog

(Magma) [n*(n-1)*(3*n^2+n-12)/4: n in [1..45]]; // Vincenzo Librandi, Jun 30 2011
(PARI) concat(0, Vec(x^2*(5*x^2-22*x-1) / (x-1)^5 + O(x^100))) \\ Colin Barker, May 28 2015

Crossrefs

Sequence in context: A158554 A379813 A267812 * A087795 A036927 A232025

Adjacent sequences: A029696 A029697 A029698 * A029700 A029701 A029702

Keyword

nonn,easy

Author

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

Status

approved