OFFSET
0,5
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..1002, flattened
N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.
FORMULA
Row 0 = {1}, row 1 = {1 1}; for n >=2, row n = row n-1 + (row floor(n/2) shifted one place right).
G.f. for column k (k >= 2): x^(2^(k-2))/((1-x)*Product_j=1..k-2} (1-x^(2^j))).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 3, 2;
1, 4, 4, 1;
1, 5, 6, 2;
1, 6, 9, 4;
1, 7, 12, 6;
1, 8, 16, 10, 1;
MAPLE
T:= proc(n) option remember;
`if`(n=0, 1, zip((x, y)-> x+y, [T(n-1)], [0, T(floor(n/2))], 0)[])
end:
seq(T(n), n=0..25); # Alois P. Heinz, Apr 01 2012
MATHEMATICA
row[0] = {1}; row[1] = {1, 1}; row[n_] := row[n] = Plus @@ PadRight[ {row[n-1], Join[{0}, row[Floor[n/2]]]} ]; Table[row[n], {n, 0, 25}] // Flatten (* Jean-François Alcover, Jan 31 2014 *)
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Dec 08 2003
EXTENSIONS
More terms from Alford Arnold, May 22 2004
STATUS
approved