login
A080881
a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=2, a(2)=10.
7
1, 2, 10, 21, 106, 223, 1126, 2369, 11962, 25167, 127078, 267361, 1350010, 2840303, 14341798, 30173889, 152359738, 320551567, 1618589926, 3405371681, 17195050234, 36176882223, 182671192870, 384324217729, 1940602920634
OFFSET
0,2
FORMULA
G.f.: (-x^3 - x^2 + 2*x + 1)/(4*x^4 - 11*x^2 + 1)
a(n + 4) = 11*a(n + 2) - 4*a(n) [From Richard Choulet, Dec 06 2008]
a(n) = (3/140*15^(1/2)*7^(1/2) + 1/4 + 3/56*7^(1/2) + 1/24*15^(1/2))*sqrt((11 + sqrt(105))/2)^n + ( - 3/140*15^(1/2)*7^(1/2) + 1/4 - 3/56*7^(1/2) + 1/24*15^(1/2))*sqrt((11 - sqrt(105))/2)^n + (3/140*15^(1/2)*7^(1/2) - 1/24*15^(1/2) - 3/56*7^(1/2) + 1/4)*( - sqrt((11 + sqrt(105))/2))^n + (1/4 + 3/56*7^(1/2) - 1/24*15^(1/2) - 3/140*15^(1/2)*7^(1/2))*( - sqrt((11 - sqrt(105))/2))^n [From Richard Choulet, Dec 07 2008]
MATHEMATICA
CoefficientList[Series[(-x^3-x^2+2x+1)/(4x^4-11x^2+1), {x, 0, 30}], x] (* or *) LinearRecurrence[ {0, 11, 0, -4}, {1, 2, 10, 21}, 30] (* Harvey P. Dale, Jun 10 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 22 2003
STATUS
approved