OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1500
Index entries for linear recurrences with constant coefficients, signature (0, 12, 0, -1).
FORMULA
G.f.: (-x^3 - 6*x^2 + x + 1)/(x^4 - 12*x^2 + 1).
a(n+4) = 12*a(n+2)-a(n). [Richard Choulet, Dec 04 2008]
a(n) = (1/4 + ((sqrt(6 + sqrt(35)) - sqrt(6 - sqrt(35)))/(4*sqrt(35))))*(sqrt(6 + sqrt(35)))^n + (1/4 + ((sqrt(6 + sqrt(35)) - sqrt(6 - sqrt(35)))/(4*sqrt(35))))*(sqrt(6 - sqrt(35)))^n + (1/4 - ((sqrt(6 + sqrt(35)) - sqrt(6 - sqrt(35)))/(4*sqrt(35))))*( - sqrt(6 + sqrt(35)))^n + (1/4 - ((sqrt(6 + sqrt(35)) - sqrt(6 - sqrt(35)))/(4*sqrt(35))))*( - (sqrt(6 - sqrt(35))))^n. [Richard Choulet, Dec 06 2008]
MATHEMATICA
LinearRecurrence[{0, 12, 0, -1}, {1, 1, 6, 11}, 30] (* Harvey P. Dale, Jul 14 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 22 2003
STATUS
approved