OFFSET
1,5
COMMENTS
LINKS
W. Duke, Stephen J. Greenfield and Eugene R. Speer, Properties of a Quadratic Fibonacci Recurrence, J. Integer Sequences, 1998, #98.1.8.
FORMULA
T(1,0)=1; T(2,0)=1; T(3,0)=T(3,1)=1; T(n,k)=0 for k >= ceiling(n/2); T(n,k) = T(n-1, k) + Sum_{j=0..k} T(n-2, j)*T(n-2, k-j) for n >= 4.
EXAMPLE
P[5,t] = 3 + 3*t + t^2; therefore T(3,0)=3, T(3,1)=3, T(3,2)=1.
Triangle begins:
1;
1;
1, 1;
2, 1;
3, 3, 1;
7, 7, 2;
16, 25, 17, 6, 1;
MAPLE
P[1]:=1:P[2]:=1:P[3]:=1+t:for n from 4 to 13 do P[n]:=sort(expand(P[n-1]+P[n-2]^2)) od:for n from 1 to 11 do seq(coeff(t*P[n], t^k), k=1..2^(ceil(n/2)-2)+1) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Mar 21 2005
STATUS
approved