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%I #48 Aug 09 2022 03:22:39
%S 0,3,4,15,12,35,24,63,40,99,60,143,84,195,112,255,144,323,180,399,220,
%T 483,264,575,312,675,364,783,420,899,480,1023,544,1155,612,1295,684,
%U 1443,760,1599,840,1763,924,1935,1012,2115,1104,2303,1200,2499,1300
%N a(n) = lcm(n+1, n-1).
%C 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
%H Harry J. Smith, <a href="/A066830/b066830.txt">Table of n, a(n) for n = 1..1000</a>
%H J. Striker and N. Williams, <a href="https://arxiv.org/abs/1108.1172">Promotion and Rowmotion</a>, arXiv preprint arXiv:1108.1172 [math.CO], 2011-2012.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F a(2n) = A000466(n); a(2n+1) = A046092(n).
%F From _Colin Barker_, Nov 05 2014: (Start)
%F a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n > 6.
%F a(n) = (3+(-1)^n)*(-1+n^2)/4.
%F G.f.: x^2*(x^4 - 6*x^2 - 4*x - 3) / ((x-1)^3*(x+1)^3).
%F (End)
%F From _Amiram Eldar_, Aug 09 2022: (Start)
%F a(n) = numerator((n^2 - 1)/2).
%F Sum_{n>=2} 1/a(n) = 1. (End)
%p A066830:=n->lcm(n+1,n-1): seq(A066830(n), n=1..100); # _Wesley Ivan Hurt_, Jul 09 2017
%t Table[LCM[n-1,n+1],{n,100}] (* _Zak Seidov_, Oct 23 2009 *)
%t a[n_] := If[EvenQ[n], n(n+2)/2, n(n+2)]; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Jun 13 2017 *)
%o (PARI) { for (n=1, 1000, write("b066830.txt", n, " ", lcm(n+1, n-1)) ) } \\ _Harry J. Smith_, Mar 30 2010
%o (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
%Y Cf. A000466, A046092.
%K nonn,easy
%O 1,2
%A _Benoit Cloitre_, Jan 20 2002
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