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Generalized meta-Fibonacci sequence a(n) with parameters s=3 and k=4.
+10
2
1, 1, 1, 1, 2, 3, 4, 4, 4, 4, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 32, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40
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]
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
a(n) = min{j : A120510(j) = n}.
+10
2
1, 5, 6, 7, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 70, 73, 74
OFFSET
1,2
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]
FORMULA
g.f.: P(z) = z / (1-z) * (1 + sum(z^(m^4) * (3 + 1 / (1 - z^(m^4))), m=0..infinity))
MAPLE
p := proc(n)
if n=1 then return 1; end if;
for j from p(n-1)+1 to infinity do
if A120510(j) = n then return j; fi; od;
end proc;
CROSSREFS
KEYWORD
nonn
AUTHOR
Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006
STATUS
approved

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