OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened
FORMULA
G.f.: G(t,z) = (1+z+z^2-tz^2)/(1-z-tz^2+tz^3-z^3). Row generating polynomials P[n] are given by P[n](t)=Q[n](t,1), where Q[0]=1, Q[1]=1+x, Q[n](t,x)=Q[n-1](t,1)+xQ[n-2](t,t) for n>=2.
EXAMPLE
T(7,2)=3 because we have 1101010, 1010101 and 0101011.
Triangle starts:
1;
2;
3;
4,1;
6,2;
9,3,1;
13,6,2;
19,11,3,1;
MAPLE
Q[0]:=1: Q[1]:=1+x: for n from 2 to 30 do Q[n]:=expand(subs(x=1, Q[n-1])+x*subs(x=t, Q[n-2])) od: for n from 0 to 18 do P[n]:=subs(x=1, Q[n]) od; 1; for n from 1 to 18 do seq(coeff(P[n], t, j), j=0..floor((n-1)/2)) od; # yields sequence in triangular form
MATHEMATICA
Flatten[CoefficientList[CoefficientList[Series[(1 + z + z^2 - t*z^2)/(1 - z - t*z^2 + t*z^3 - z^3), {z, 0, 20}, {t, 0, 20}], z], t]] (* G. C. Greubel, May 02 2017 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, May 12 2007
STATUS
approved