OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 6, 0, -4).
FORMULA
G.f.: (-3*x^3 - 4*x^2 + x + 1)/(4*x^4 - 6*x^2 + 1)
a(n + 4) = 6*a(n + 2) - 4*a(n) [From Richard Choulet, Dec 06 2008]
a(n) = ( - 1/20*5^(1/2) + 1/16*5^(1/2)*2^(1/2) - 1/16*2^(1/2) + 1/4)*(sqrt(3 + sqrt(5)))^n + (1/20*5^(1/2) + 1/16*5^(1/2)*2^(1/2) + 1/16*2^(1/2) + 1/4)*(sqrt(3 - sqrt(5)))^n + ( - 1/20*5^(1/2) - 1/16*5^(1/2)*2^(1/2) + 1/16*2^(1/2) + 1/4)*( - (sqrt(3 + sqrt(5))))^n + (1/20*5^(1/2) - 1/16*5^(1/2)*2^(1/2) - 1/16*2^(1/2) + 1/4)*( - (sqrt(3 - sqrt(5))))^n [From Richard Choulet, Dec 07 2008]
MATHEMATICA
LinearRecurrence[{0, 6, 0, -4}, {1, 1, 2, 3}, 50] (* or *) CoefficientList[ Series[ (-3x^3-4x^2+x+1)/(4x^4-6x^2+1), {x, 0, 50}], x] (* Harvey P. Dale, May 02 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 22 2003
STATUS
approved