OFFSET
0,2
COMMENTS
If n == 2 or 4 (mod 6) then a(n) = 3*n/2; if n == 3 (mod 6) then a(n) = 2*n/3; if n == 1 or 5 (mod 6) then a(n) = 6*n; otherwise, a(n) = n/6. Examples: n = 50 = 6*8+2, a(50) = 3*50/2 = 75; n = 23 = 6*3+5, a(23) = 6*23 = 138. - Bruno Berselli, Mar 08 2017
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2,0,0,0,0,0,-1).
FORMULA
G.f.: x*(6 + 3*x + 2*x^2 + 6*x^3 + 30*x^4 + x^5 + 30*x^6 + 6*x^7 + 2*x^8 + 3*x^9 + 6*x^10) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)^2*(1 + x + x^2)^2).
a(n) = 2*a(n-6) - a(n-12) for n>11.
Sum_{k=1..n} a(k) ~ (95/72)*n^2. - Amiram Eldar, Oct 07 2023
MATHEMATICA
Table[LCM[n, 6] / GCD[n, 6], {n, 0, 63}] (* Indranil Ghosh, Mar 08 2017 *)
PROG
(PARI) concat(0, Vec(x*(6 + 3*x + 2*x^2 + 6*x^3 + 30*x^4 + x^5 + 30*x^6 + 6*x^7 + 2*x^8 + 3*x^9 + 6*x^10) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)^2*(1 + x + x^2)^2) + O(x^100)))
(PARI) {for (n=0, 63, print1((lcm(n, 6) / gcd(n, 6)), ", "))}; \\ Indranil Ghosh, Mar 08 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 07 2017
STATUS
approved