OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,-12,7,4,-4).
FORMULA
a(n+5) = 6*a(n+4)-12*a(n+3)+7*a(n+2)+4*a(n+1)-4*a(n).
a(n) = (38/5*5^(1/2)+17)*((1+sqrt(5))/2)^n+(-38/5*5^(1/2)+17)*((1-sqrt(5))/2)^n-32*2^n-1+16*2^(n-1)*n.
a(n) = F(n+8)+2^(n+3)*(n-4)-1, where (F(n)) is the Fibonacci sequence for which F(0)=F(1)=1, F(2)=2, ... (related to A000045).
MAPLE
c(0):=1:c(1):=6:c(2):=24:c(3):=79:c(4):=232:for n from 0 to 30 do : c(n+5):=6*c(n+4)-12*c(n+3)+7*c(n+2)+4*c(n+1)-4*c(n): od :seq(c(n), n=0..30); taylor((-1/(-1+z)/(-1+2*z)^2/(1-z-z^2)), z=0, 30); for n from 0 to 30 do a(n):=simplify((38/5*5^(1/2)+17)*((1+sqrt(5))/2)^n+(-38/5*5^(1/2)+17)*((1-sqrt(5))/2)^n-32*2^n-1+16*2^(n-1)*n):od:seq(a(n), n=0..30);
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Feb 07 2010
STATUS
approved