A221921 a(n) = 4*n/gcd(4*n,n+4), n >= 4.

2, 20, 12, 28, 8, 36, 20, 44, 3, 52, 28, 60, 16, 68, 36, 76, 10, 84, 44, 92, 24, 100, 52, 108, 7, 116, 60, 124, 32, 132, 68, 140, 18, 148, 76, 156, 40, 164, 84, 172, 11, 180, 92, 188, 48, 196, 100, 204, 26, 212, 108, 220, 56, 228, 116, 236, 15, 244, 124, 252, 64

Offset

4,1

Comments

This is the fourth column of the triangle A221918.

Links

Table of n, a(n) for n=4..64.

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

Cf. A221918, A000027 (m=1), A145979(m=2), A221920 (m=3).

Sequence in context: A058403 A083297 A343927 * A012739 A261753 A075031

Adjacent sequences: A221918 A221919 A221920 * A221922 A221923 A221924

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 21 2013

Status

approved