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
Examples
a(6) = 28 as lcm(6,7,8)/6 = 168/6 = 28.
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.
Programs
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Haskell
a067046 = (`div` 6) . a033931 -- Reinhard Zumkeller, Jul 04 2012
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Mathematica
Table[LCM[n,n+1,n+2]/6,{n,50}] (* Harvey P. Dale, Jan 11 2011 *) -
PARI
a(n)={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
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)