OFFSET
0,4
COMMENTS
A Fibonacci tree of order n (n>=2) is a complete binary tree whose left subtree is the Fibonacci tree of order n-1 and whose right subtree is the Fibonacci tree of order n-2; each of the Fibonacci trees of order 0 and 1 is defined as a single node.
Sum of entries in row n is A001595(n).
Sum_{k=0..n-1} k*T(n,k) = A178523(n).
REFERENCES
D. E. Knuth, The Art of Computer Programming, Vol. 3, 2nd edition, Addison-Wesley, Reading, MA, 1998, p. 417.
LINKS
Y. Horibe, An entropy view of Fibonacci trees, Fibonacci Quarterly, 20, No. 2, 1982, 168-178.
FORMULA
G.f.: G(t,z)=(1-tz+tz^2)/[(1-z)(1-tz-tz^2)].
T(k,n) = T(k-1,n-1)+T(k-1,n) with T(0,0)=1, T(k,0)=1 for k>0, T(0,n)=2 for n>0. - Frank M Jackson, Aug 30 2011
EXAMPLE
Triangle starts:
1,
1,
1,2,
1,2,2,
1,2,4,2,
1,2,4,6,2,
1,2,4,8,8,2,
1,2,4,8,14,10,2,
1,2,4,8,16,22,12,2,
1,2,4,8,16,30,32,14,2,
...
MAPLE
G := (1-t*z+t*z^2)/((1-z)*(1-t*z-t*z^2)): Gser := simplify(series(G, z = 0, 17)): for n from 0 to 15 do P[n] := sort(coeff(Gser, z, n)) end do: 1; for n to 13 do seq(coeff(P[n], t, k), k = 0 .. n-1) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Jun 15 2010
STATUS
approved