OFFSET
4,1
COMMENTS
This is the fourth column of the triangle A221918.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).
FORMULA
a(n) = A221918(n,4) = numerator(n*4/(n+4)), n >= 4.
a(n) = 4*n/gcd(16,n+4), n >= 4.
G.f.: x^4*(-12*x^31 - 4*x^30 - 4*x^29 + 4*x^27 + 4*x^26 + 12*x^25 + x^24 + 20*x^23 + 12*x^22 + 28*x^21 + 8*x^20 + 36*x^19 + 20*x^18 + 44*x^17 + 6*x^16 + 76*x^15 + 36*x^14 + 68*x^13 + 16*x^12 + 60*x^11 + 28*x^10 + 52*x^9 + 3*x^8 + 44*x^7 + 20*x^6 + 36*x^5 + 8*x^4 + 28*x^3 + 12*x^2 + 20*x + 2) / (x^32 - 2*x^16 + 1). - Colin Barker, Feb 25 2013
Sum_{k=4..n} a(k) ~ (171/128) * n^2. - Amiram Eldar, Oct 09 2023
EXAMPLE
a(8) = numerator(32/12) = numerator(8/3) = 8 = 32/gcd(32,12) = 32/4 = 32/gcd(16,12).
MATHEMATICA
Table[(4n)/GCD[4n, n+4], {n, 4, 70}] (* Harvey P. Dale, May 15 2018 *)
PROG
(PARI) a(n)=4*n/gcd(4*n, n+4) \\ Charles R Greathouse IV, Apr 18 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 21 2013
STATUS
approved