A066830 a(n) = lcm(n+1, n-1).

0, 3, 4, 15, 12, 35, 24, 63, 40, 99, 60, 143, 84, 195, 112, 255, 144, 323, 180, 399, 220, 483, 264, 575, 312, 675, 364, 783, 420, 899, 480, 1023, 544, 1155, 612, 1295, 684, 1443, 760, 1599, 840, 1763, 924, 1935, 1012, 2115, 1104, 2303, 1200, 2499, 1300

Offset: 1

Author

Benoit Cloitre, Jan 20 2002

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000466, A046092.

Programs

Maple

A066830:=n->lcm(n+1,n-1): seq(A066830(n), n=1..100); # Wesley Ivan Hurt, Jul 09 2017

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 *)

PARI

a(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

Formula

a(2n) = A000466(n); a(2n+1) = A046092(n).

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)

E.g.f.: (2 - (2 - x - 2*x^2)*cosh(x) - (1 - 2*x - x^2)*sinh(x))/2. - Stefano Spezia, Aug 04 2025