A067046 a(n) = lcm(n, n+1, n+2)/6.

1, 2, 10, 10, 35, 28, 84, 60, 165, 110, 286, 182, 455, 280, 680, 408, 969, 570, 1330, 770, 1771, 1012, 2300, 1300, 2925, 1638, 3654, 2030, 4495, 2480, 5456, 2992, 6545, 3570, 7770, 4218, 9139, 4940, 10660, 5740, 12341, 6622, 14190, 7590, 16215, 8648, 18424, 9800

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Amarnath Murthy, Some Notions on Least Common Multiples, Smarandache Notions Journal, Vol. 12, No. 1-2-3 (Spring 2001), pp. 307-308.

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

Index entries for sequences related to lcm's.

Formula

G.f.: (x^4 + 2x^3 + 6x^2 + 2x + 1)/(1 - x^2)^4.

a(n) = binomial(n+2,3)*(3-(-1)^n)/4. - Gary Detlefs, Apr 13 2011

Quasipolynomial: a(n) = n(n+1)(n+2)/6 when n is odd and n(n+1)(n+2)/12 otherwise. - Charles R Greathouse IV, Feb 27 2012

a(n) = A033931(n) / 6. - Reinhard Zumkeller, Jul 04 2012

From Amiram Eldar, Sep 29 2022: (Start)

Sum_{n>=1} 1/a(n) = 6*(1 - log(2)).

Sum_{n>=1} (-1)^(n+1)/a(n) = 6*(3*log(2) - 2). (End)

Example

a(6) = 28 as lcm(6,7,8)/6 = 168/6 = 28.

Mathematica

Table[LCM[n, n+1, n+2]/6, {n, 50}] (* Harvey P. Dale, Jan 11 2011 *)

Prog

(PARI) { for (n=1, 1000, write("b067046.txt", n, " ", lcm(lcm(n, n+1), n+2)/6) ) } \\ Harry J. Smith, Apr 30 2010
(PARI) a(n)=binomial(n+2, 3)/(2-n%2) \\ Charles R Greathouse IV, Feb 27 2012
(Haskell)
a067046 = (`div` 6) . a033931  -- Reinhard Zumkeller, Jul 04 2012

Crossrefs

Cf. A000447 (bisection), A006331 (bisection), A033931.

Sequence in context: A212621 A156780 A206486 * A066394 A232500 A351659

Adjacent sequences: A067043 A067044 A067045 * A067047 A067048 A067049

Keyword

nonn,easy

Author

Amarnath Murthy, Dec 30 2001

Status

approved