OFFSET
1,5
LINKS
C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences, J. Integer Seq., Vol. 12. [This is a later version than that in the GenMetaFib.html link]
C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences
FORMULA
If 1 <= n <= 4, a(n)=1. If 5 <= n <= 7, then a(n)=n-3. If n>7 then a(n)=a(n-3-a(n-1)) + a(n-4-a(n-2)) + a(n-5-a(n-3)) + a(n-6-a(n-4)).
G.f.: A(z) = z * (1 - z^3) / (1 - z) * sum(prod(z^3 * (1 - z^(4 * [i])) / (1 - z^[i]), i=1..n), n=0..infinity), where [i] = (4^i - 1) / 3.
MAPLE
a := proc(n)
option remember;
if n <= 4 then return 1 end if;
if n <= 7 then return n-3 end if;
return add(a(n - i - 2 - a(n - i)), i = 1 .. 4)
end proc
CROSSREFS
KEYWORD
nonn
AUTHOR
Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006
STATUS
approved