OFFSET
1,2
COMMENTS
Row sums of triangle A130154. Also, binomial transform of [1, 1, 2, 2, 0, 0, 0, ...]. - Gary W. Adamson, Oct 23 2007
Conjecture: also counts the distinct pairs (flips, iterations) that a bubble sort program generates when sorting all permutations of 1..n. - Wouter Meeussen, Dec 13 2008
a(n) is the number of lattice points (x,y) in the closed region bounded by the parabolas y = x*(x - n) and y = x*(n - x). - Clark Kimberling, Jun 01 2013
LINKS
Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
Sergey Kitaev, Jeffrey Remmel, and Mark Tiefenbruck, Quadrant Marked Mesh Patterns in 132-Avoiding Permutations II, arXiv:1302.2274 [math.CO], 2013.
Sergey Kitaev, Jeffrey Remmel, and Mark Tiefenbruck, Quadrant Marked Mesh Patterns in 132-Avoiding Permutations II, Integers: Electronic Journal of Combinatorial Number Theory, 15 (2015), #A16.
Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1)
FORMULA
G.f.: (3*x^2 - 2*x + 1)*x/(x - 1)^4.
a(n) = (n^3 - 3*n^2 + 5*n)/3. - Franklin T. Adams-Watters, Sep 13 2006
a(n) = A006527(n-1) + 1. - Vladimir Joseph Stephan Orlovsky, May 04 2011
E.g.f.: exp(x)*(x + x^3/3). - Nikolaos Pantelidis, Feb 05 2023
MATHEMATICA
Table[(n^3-3*n^2+5*n)/3, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, May 04 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
EXTENSIONS
More terms from Franklin T. Adams-Watters, Sep 13 2006
STATUS
approved