OFFSET
1,2
COMMENTS
a(n+2) is the order of rowmotion on a poset obtained by adjoining a unique minimal and maximal element to a disjoint union of at least two chains of n elements. - Nick Mayers, Jun 01 2018
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
J. Striker and N. Williams, Promotion and Rowmotion, arXiv preprint arXiv:1108.1172 [math.CO], 2011-2012.
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
FORMULA
From Colin Barker, Nov 05 2014: (Start)
a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n > 6.
a(n) = (3+(-1)^n)*(-1+n^2)/4.
G.f.: x^2*(x^4 - 6*x^2 - 4*x - 3) / ((x-1)^3*(x+1)^3).
(End)
From Amiram Eldar, Aug 09 2022: (Start)
a(n) = numerator((n^2 - 1)/2).
Sum_{n>=2} 1/a(n) = 1. (End)
MAPLE
MATHEMATICA
Table[LCM[n-1, n+1], {n, 100}] (* Zak Seidov, Oct 23 2009 *)
a[n_] := If[EvenQ[n], n(n+2)/2, n(n+2)]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jun 13 2017 *)
PROG
(PARI) { for (n=1, 1000, write("b066830.txt", n, " ", lcm(n+1, n-1)) ) } \\ Harry J. Smith, Mar 30 2010
(PARI) concat(0, Vec(x^2*(x^4-6*x^2-4*x-3)/((x-1)^3*(x+1)^3) + O(x^100))) \\ Colin Barker, Nov 05 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Jan 20 2002
STATUS
approved