|
| |
|
|
A221920
|
|
a(n) = 3*n/gcd(3*n, n+3), n >= 3.
|
|
3
|
|
|
|
3, 12, 15, 2, 21, 24, 9, 30, 33, 12, 39, 42, 5, 48, 51, 18, 57, 60, 21, 66, 69, 8, 75, 78, 27, 84, 87, 30, 93, 96, 11, 102, 105, 36, 111, 114, 39, 120, 123, 14, 129, 132, 45, 138, 141, 48, 147, 150, 17, 156, 159, 54, 165, 168, 57, 174, 177, 20, 183, 186, 63
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
3,1
|
|
|
COMMENTS
|
This is the third column sequence (m = 3) of the triangle A221918.
|
|
|
LINKS
|
Table of n, a(n) for n=3..63.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-1).
|
|
|
FORMULA
|
a(n) = A221918(n,3) = numerator(n*3/(n+3)), n >= 3.
a(n) = 3*n/gcd(3*n,n+3), n >= 3.
a(n) = 3*n/gcd(9,n+3), n >= 3, (because gcd(n+3,3*n) = gcd(n+3,3*n - 3*(n+3)) = gcd(n+3,-3^2) = gcd(n+3,9)).
G.f.: -x^3*(6*x^17 + 3*x^16 - 3*x^14 - 6*x^13 - x^12 - 12*x^11 - 15*x^10 - 6*x^9 - 33*x^8 - 30*x^7 - 9*x^6 - 24*x^5 - 21*x^4 - 2*x^3 - 15*x^2 - 12*x - 3) / ((x-1)^2*(x^2 + x + 1)^2*(x^6 + x^3 + 1)^2). [Colin Barker, Feb 25 2013]
|
|
|
EXAMPLE
|
a(6) = numerator(18/9) = numerator(2) = 2 = 18/gcd(18,9) = 18/9 = 18/gcd(9,9) = 18/9.
|
|
|
PROG
|
(PARI) a(n)=3*n/gcd(3*n, n+3) \\ Charles R Greathouse IV, Apr 18 2013
|
|
|
CROSSREFS
|
Cf. A221918, A000027 (m=1), A145979(m=2), A221921 (m=4), A222463 (m=5).
Sequence in context: A039945 A227302 A201273 * A349663 A188549 A287357
Adjacent sequences: A221917 A221918 A221919 * A221921 A221922 A221923
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Wolfdieter Lang, Feb 21 2013
|
|
|
STATUS
|
approved
|
| |
|
|
