OFFSET
1,2
COMMENTS
Also number of permutations of length n which avoid the patterns 321, 2134 (reverse symmetry); or 321, 1243 (complement symmetry); etc.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Christian Bean, Bjarki Gudmundsson, Henning Ulfarsson, Automatic discovery of structural rules of permutation classes, arXiv:1705.04109 [math.CO], 2017.
Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: x*(2*x^3 - 5*x^2 + 3*x - 1)/(x-1)^5.
a(n) = (n^4 + 2*n^3 - 13*n^2 + 34*n)/24. - Franklin T. Adams-Watters, Sep 16 2006
Partial sums of A105163. - Levi R. Self (levi.r.self(AT)gmail.com), Aug 04 2007
Binomial transform of [1, 1, 2, 3, 1, 0, 0, 0, ...]. - Gary W. Adamson, Oct 23 2007
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 2, 5, 13, 30}, 50] (* Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)
CoefficientList[Series[(2 x^3 - 5 x^2 + 3 x - 1)/(x - 1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Nov 01 2014 *)
PROG
(PARI) for(n=1, 100, print1((n^4 + 2*n^3 - 13*n^2 + 34*n)/24", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 22 2008
(Magma) [(n^4 + 2*n^3 - 13*n^2 + 34*n)/24: n in [1..45]]; // Vincenzo Librandi, Nov 01 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
EXTENSIONS
Edited by N. J. A. Sloane, Mar 16 2008
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 22 2008
STATUS
approved