A282284 Least common multiple of 3*n+1 and 3*n-1.

1, 4, 35, 40, 143, 112, 323, 220, 575, 364, 899, 544, 1295, 760, 1763, 1012, 2303, 1300, 2915, 1624, 3599, 1984, 4355, 2380, 5183, 2812, 6083, 3280, 7055, 3784, 8099, 4324, 9215, 4900, 10403, 5512, 11663, 6160, 12995, 6844, 14399, 7564, 15875, 8320, 17423

Offset: 0

Author

Colin Barker, Feb 11 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

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))

Formula

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

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

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

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).