A061506 a(n) = lcm(6n+2, 6n+4, 6n+6).

12, 120, 1008, 1320, 5460, 4896, 15960, 12144, 35100, 24360, 65472, 42840, 109668, 68880, 170280, 103776, 249900, 148824, 351120, 205320, 476532, 274560, 628728, 357840, 810300, 456456, 1023840, 571704, 1271940, 704880, 1557192, 857280, 1882188, 1030200

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).

Formula

G.f.: (120*x^6 + 336*x^5 + 1500*x^4 + 840*x^3 + 960*x^2 + 120*x + 12)/((x-1)^4*(x+1)^4). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

a(n) = 4*a(n-2) - 6*a(n-4) + 4*a(n-6) - a(n-8), a(0)=12, a(1)=120, a(2)=1008, a(3)=1320, a(4)=5460, a(5)=4896, a(6)=15960, a(7)=12144. - Harvey P. Dale, Oct 22 2012

From Colin Barker, Mar 13 2017: (Start)

a(n) = 6*(3*n + 1)*(3*n + 2)*(n + 1) for n even.

a(n) = 3*(3*n + 1)*(3*n + 2)*(n + 1) for n odd.

(End)

From Amiram Eldar, Oct 08 2023: (Start)

Sum_{n>=0} 1/a(n) = 11*sqrt(3)*Pi/144 - log(2)/6 - 3*log(3)/16.

Sum_{n>=0} (-1)^n/a(n) = log(3)/16 + log(2)/2 - Pi*sqrt(3)/16. (End)

Example

lcm(2, 4, 6) = 12; lcm(8, 10, 12) = 120.

Mathematica

Table[LCM@@(6n+{2, 4, 6}), {n, 0, 40}] (* or *) LinearRecurrence[ {0, 4, 0, -6, 0, 4, 0, -1}, {12, 120, 1008, 1320, 5460, 4896, 15960, 12144}, 40] (* Harvey P. Dale, Oct 22 2012 *)

Prog

(PARI) Vec(12*(1 + 10*x + 80*x^2 + 70*x^3 + 125*x^4 + 28*x^5 + 10*x^6) / ((1 - x)^4*(1 + x)^4) + O(x^50)) \\ Colin Barker, Mar 13 2017
(Magma) [Lcm([6*n+2, 6*n+4, 6*n+6]): n in [0..35]]; // Vincenzo Librandi, Mar 18 2018

Crossrefs

Cf. A005843.

Sequence in context: A009050 A067358 A268634 * A059155 A012443 A012274

Adjacent sequences: A061503 A061504 A061505 * A061507 A061508 A061509

Keyword

easy,nonn

Author

Jason Earls, Jun 12 2001

Status

approved