OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (0, 8, 0, -1).
FORMULA
a(n) = (3 + a(n-1)*a(n-2))/a(n-3) for n>2.
G.f.: (-x^3 - 4*x^2 + x + 1)/(x^4 - 8*x^2 + 1)
a(n+4) = 8*a(n+2)-a(n). - Richard Choulet, Dec 04 2008
a(n) = (0.25 + sqrt(10)/20)*(sqrt(4 + sqrt(15)))^n + (0.25 + sqrt(10)/20)*(sqrt(4 - sqrt(15)))^n + ( - 1/20*10^(1/2) + 1/4)*( - sqrt(4 + sqrt(15)))^n + ( - 1/20*10^(1/2) + 1/4)*( - (sqrt(4 - sqrt(15))))^n. - Richard Choulet, Dec 06 2008
MATHEMATICA
RecurrenceTable[{a[0]==a[1]==1, a[2]==4, a[n]==(3+a[n+1]a[n+2])/a[n+3]}, a, {n, 30}] (* Harvey P. Dale, Jun 08 2017 *)
PROG
(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 0, 8, 0]^n*[1; 1; 4; 7])[1, 1] \\ Charles R Greathouse IV, May 17 2026
(PARI) Vec((-x^3-4*x^2+x+1)/(x^4-8*x^2+1)+O(x^99)) \\ Charles R Greathouse IV, May 17 2026
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Paul D. Hanna, Feb 22 2003
STATUS
approved
