OFFSET
1,1
COMMENTS
LINKS
Alois P. Heinz, Rows n = 1..150, flattened
FORMULA
G.f.: G(t,z) = (1+z-tz+z^2)/(1-z-tz+tz^2-z^3)-1.
EXAMPLE
T(5,2)=3 because we have 00011, 10001 and 11000.
Triangle starts:
2;
3, 1;
4, 2, 1;
6, 3, 2, 1;
9, 6, 3, 2, 1;
13, 11, 7, 3, 2, 1;
MAPLE
G:=(1+z-t*z+z^2)/(1-z-t*z+t*z^2-z^3)-1: Gser:=simplify(series(G, z=0, 14)): for n to 12 do P[n]:=sort(coeff(Gser, z, n)) end do: for n to 12 do seq(coeff(P[n], t, j), j=0..n-1) end do; # yields sequence in triangular form
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<3,
expand(b(n-1, i+1) +b(n-1, i)*`if`(i=2, x, 1)), b(n-1, 1)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n, 1)):
seq(T(n), n=0..15); # Alois P. Heinz, Dec 18 2013
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<3, Expand[b[n-1, i+1] + b[n-1, i]*If[i == 2, x, 1]], b[n-1, 1]]]; T[n_] := Function[{p}, Table[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][b[n, 1]]; Table[T[n], {n, 1, 15}] // Flatten (* Jean-François Alcover, Feb 19 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Aug 15 2008
STATUS
approved