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A067047
a(n) = lcm(n, n+1, n+2, n+3)/12.
5
1, 5, 5, 35, 70, 42, 210, 330, 165, 715, 1001, 455, 1820, 2380, 1020, 3876, 4845, 1995, 7315, 8855, 3542, 12650, 14950, 5850, 20475, 23751, 9135, 31465, 35960, 13640, 46376, 52360, 19635, 66045, 73815, 27417, 91390, 101270, 37310, 123410, 135751, 49665, 163185
OFFSET
1,2
LINKS
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 (0,0,5,0,0,-10,0,0,10,0,0,-5,0,0,1).
FORMULA
Quasipolynomial: a(n) = n(n+1)(n+2)(n+3)/72 if 3|n and a(n) = n(n+1)(n+2)(n+3)/24 otherwise.
a(n) = n*(n+1)*(n+2)*(n+3)/(8*(5+4*cos(2*n*Pi/3))). - Gary Detlefs, Apr 01 2011
G.f.: -x*(x^10 + 5*x^9 + 5*x^8 + 30*x^7 + 45*x^6 + 17*x^5 + 45*x^4 + 30*x^3 + 5*x^2 + 5*x+1)/ ((x-1)^5*(x^2+x+1)^5). - Colin Barker, Jul 01 2012
From Amiram Eldar, Sep 29 2022: (Start)
Sum_{n>=1} 1/a(n) = 16 - 8*Pi/sqrt(3).
Sum_{n>=1} (-1)^(n+1)/a(n) = 160*log(2)/3 - 36. (End)
EXAMPLE
a(6) = 42 as lcm(6,7,8,9)/12 = 72*7/12 = 42.
MATHEMATICA
Table[LCM@@Range[n, n+3]/12, {n, 40}] (* or *) LinearRecurrence[{0, 0, 5, 0, 0, -10, 0, 0, 10, 0, 0, -5, 0, 0, 1}, {1, 5, 5, 35, 70, 42, 210, 330, 165, 715, 1001, 455, 1820, 2380, 1020}, 40] (* Harvey P. Dale, Dec 04 2016 *)
PROG
(PARI) { for (n=1, 1000, write("b067047.txt", n, " ", lcm(lcm(n, n+1), lcm(n+2, n+3))/12) ) } \\ Harry J. Smith, May 01 2010
(PARI) a(n)=binomial(n+3, 4)/if(n%3, 1, 3) \\ Charles R Greathouse IV, Feb 28 2012
CROSSREFS
Cf. A067046.
Sequence in context: A355952 A232982 A160555 * A374508 A375993 A271054
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Dec 30 2001
STATUS
approved