%I #11 Sep 05 2020 19:35:10

%S 1,4,35,40,143,112,323,220,575,364,899,544,1295,760,1763,1012,2303,

%T 1300,2915,1624,3599,1984,4355,2380,5183,2812,6083,3280,7055,3784,

%U 8099,4324,9215,4900,10403,5512,11663,6160,12995,6844,14399,7564,15875,8320,17423

%N Least common multiple of 3*n+1 and 3*n-1.

%H Colin Barker, <a href="/A282284/b282284.txt">Table of n, a(n) for n = 0..1000</a>

%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(n) = 9*n^2-1 for n>0 and even.

%F a(n) = (9*n^2-1)/2 for n odd.

%F a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>6.

%F G.f.: (1+4*x+32*x^2+28*x^3+41*x^4+4*x^5-2*x^6) / ((1-x)^3*(1+x)^3).

%t Table[LCM@@{3n+1,3n-1},{n,0,50}] (* or *) LinearRecurrence[{0,3,0,-3,0,1},{1,4,35,40,143,112,323},60] (* _Harvey P. Dale_, Sep 05 2020 *)

%o (PARI) vector(60, n, n--; lcm(3*n+1, 3*n-1))

%o (PARI) Vec((1+4*x+32*x^2+28*x^3+41*x^4+4*x^5-2*x^6) / ((1-x)^3*(1+x)^3) + O(x^60))

%Y Cf. A000466, A136017, A141759, A282285, A282286.

%K nonn,easy

%O 0,2

%A _Colin Barker_, Feb 11 2017