OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).
FORMULA
a(n) = 2*a(n-4) - a(n-8) for n>7.
a(n) = (4*A061037(n+2))/(n+4).
a(n) = 4*n / A146160(n).
a(2*n) = A064680(n).
a(1+2*n) = A017113(n).
a(4*n) = a(-4+4*n) + 1.
a(1+4*n) = a(-3+4*n) + 16.
a(2+4*n) = a(-2+4*n) + 4.
a(3+4*n) = a(-1+4*n) + 16. See A177499.
From Bruno Berselli, Mar 22 2011: (Start)
G.f.: x*(4+2*x+12*x^2+x^3+12*x^4+2*x^5+4*x^6)/(1-x^4)^2.
a(n) = (64-3*(1+(-1)^n)*(9+i^n))*n/16 with i=sqrt(-1).
a(n)/a(n-4) = n/(n-4) for n>4. (End)
a(n) = 8*n/(11 + 9*cos(Pi*n) + 12*cos(n*Pi/2)). - Wesley Ivan Hurt, Jul 06 2016
a(n) = lcm(4,n)/gcd(4,n). - R. J. Mathar, Feb 12 2019
Sum_{k=1..n} a(k) ~ (37/32)*n^2. - Amiram Eldar, Oct 07 2023
MAPLE
A188134:=n->8*n/(11 + 9*cos(Pi*n) + 12*cos(n*Pi/2)): seq(A188134(n), n=0..100); # Wesley Ivan Hurt, Jul 06 2016
MATHEMATICA
Table[8 n/(11 + 9 Cos[Pi*n] + 12 Cos[n*Pi/2]), {n, 0, 80}] (* Wesley Ivan Hurt, Jul 06 2016 *)
CoefficientList[Series[x*(4+2*x+12*x^2+x^3+12*x^4+2*x^5+4*x^6)/(1-x^4)^2, {x, 0, 50}], x] (* G. C. Greubel, Sep 20 2018 *)
LinearRecurrence[{0, 0, 0, 2, 0, 0, 0, -1}, {0, 4, 2, 12, 1, 20, 6, 28}, 70] (* Harvey P. Dale, Aug 14 2019 *)
PROG
(Magma) [(64-3*(1+(-1)^n)*(9+(-1)^(n div 2)))*n/16 : n in [0..80]]; // Wesley Ivan Hurt, Jul 06 2016
(PARI) x='x+O('x^50); concat([0], Vec(x*(4+2*x+12*x^2+x^3+12*x^4+ 2*x^5 +4*x^6)/(1-x^4)^2)) \\ G. C. Greubel, Sep 20 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Mar 21 2011
STATUS
approved