OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).
FORMULA
a(n) = lcm(n + 4, n) / gcd(n + 4, n).
From Colin Barker, Mar 27 2017: (Start)
G.f.: x*(5 + 3*x + 21*x^2 + 2*x^3 + 30*x^4 + 6*x^5 + 14*x^6 - 3*x^8 - x^9 - 3*x^10) / ((1 - x)^3*(1 + x)^3*(1 + x^2)^3).
a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12) for n>12. (End)
From Luce ETIENNE, May 10 2018: (Start)
a(n) = n*(n+4)*4^((5*(n mod 4)^3 - 24*(n mod 4)^2 + 31*(n mod 4)-12)/6).
a(n) = n*(n+4)*(37-27*cos(n*Pi)-6*cos(n*Pi/2))/64. (End)
From Amiram Eldar, Oct 08 2023: (Start)
Sum_{n>=1} 1/a(n) = 11/6.
Sum_{n>=1} (-1)^n/a(n) = 7/6.
Sum_{k=1..n} a(k) ~ (37/192) * n^3. (End)
MATHEMATICA
Table[ LCM[i + 4, i] / GCD[i + 4, i], {i, 1, 60}]
LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {5, 3, 21, 2, 45, 15, 77, 6, 117, 35, 165, 12}, 90] (* Harvey P. Dale, Jul 13 2019 *)
PROG
(PARI) Vec(x*(5 + 3*x + 21*x^2 + 2*x^3 + 30*x^4 + 6*x^5 + 14*x^6 - 3*x^8 - x^9 - 3*x^10) / ((1 - x)^3*(1 + x)^3*(1 + x^2)^3) + O(x^60)) \\ Colin Barker, Mar 27 2017
(PARI) a(n) = lcm(n+4, n)/gcd(n+4, n); \\ Altug Alkan, Sep 20 2018
(Magma) [LCM(n + 4, n)/GCD(n + 4, n): n in [1..50]]; // G. C. Greubel, Sep 20 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, May 09 2002
EXTENSIONS
Edited by Robert G. Wilson v, May 10 2002
STATUS
approved