OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).
FORMULA
a(n) = lcm(n + 3, n) / gcd(n + 3, n).
From Colin Barker, Mar 27 2017: (Start)
G.f.: 2*x*(2 + 5*x + x^2 + 8*x^3 + 5*x^4 - x^6 - x^7) / ((1 - x)^3*(1 + x + x^2)^3).
a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) for n>9.
(End)
From Amiram Eldar, Oct 08 2023: (Start)
Sum_{n>=1} 1/a(n) = 3/2.
Sum_{n>=1} (-1)^n/a(n) = 22*log(2)/9 - 7/6.
Sum_{k=1..n} a(k) ~ (19/81) * n^3. (End)
MATHEMATICA
Table[ LCM[i + 3, i] / GCD[i + 3, i], {i, 1, 60}]
PROG
(PARI) Vec(2*x*(2 + 5*x + x^2 + 8*x^3 + 5*x^4 - x^6 - x^7) / ((1 - x)^3*(1 + x + x^2)^3) + O(x^60)) \\ Colin Barker, Mar 27 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, May 09 2002
EXTENSIONS
Edited by Robert G. Wilson v, May 10 2002
STATUS
approved