OFFSET
0,5
LINKS
Alois P. Heinz, Rows n = 0..1094, flattened
N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.
FORMULA
G.f.: (1/(1-x))*(1+Sum(y^(k+1)*x^(2^(k+1)-1)/Product(1-x^(2^j), j=0..k), k=0..infinity)).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2;
1, 3, 1;
1, 4, 2;
1, 5, 4;
1, 6, 6;
1, 7, 9, 1;
MAPLE
T:= proc(n) option remember; `if`(n=0, 1,
zip((x, y)-> x+y, [T(n-1)], [0, T(floor((n-1)/2))], 0)[])
end:
seq(T(n), n=0..25); # Alois P. Heinz, Apr 01 2012
MATHEMATICA
row[0] = {1}; row[n_] := row[n] = PadRight[{row[n-1], Join[{0}, row[Floor[(n-1)/2]]]}] // Total; Table[row[n], {n, 0, 25}] // Flatten (* Jean-François Alcover, Nov 27 2014 *)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
N. J. A. Sloane, Dec 08 2003
EXTENSIONS
More terms from Vladeta Jovovic, Dec 10 2003
STATUS
approved