OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: f such that: f(z)=1/(1-2*z+z^9).
a(n) = sum((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j),j=0..floor(n/(k+1))) with k=8.
Recurrence relation: a(n+9) = 2*a(8) - a(n).
EXAMPLE
a(7)=C(7,7)*2^7=128. a(10)=C(10,10)*2^10-C(2,1)*2^1=1020.
MAPLE
for k from 0 to 20 do for n from 0 to 30 do b(n):=sum((-1)^j*binomial(n-k*j, n-(k+1)*j)*2^(n-(k+1)*j), j=0..floor(n/(k+1))):od:k: seq(b(n), n=0..30):od; k:=8:taylor(1/(1-2*z+z^(k+1)), z=0, 30);
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Jan 31 2010
STATUS
approved