A067047 a(n) = lcm(n, n+1, n+2, n+3)/12.

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

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 (0,0,5,0,0,-10,0,0,10,0,0,-5,0,0,1).

Index entries for sequences related to lcm's.

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 * A271054 A270569 A270290

Adjacent sequences: A067044 A067045 A067046 * A067048 A067049 A067050

Keyword

nonn,easy

Author

Amarnath Murthy, Dec 30 2001

Status

approved