OFFSET
0,10
COMMENTS
Significance of triangle suggested by Franklin T. Adams-Watters on Dec 19 2009. Row N has N terms in this sequence. The triangle starts:
1;
0, 1;
0, 0, 1;
0, 0, 1, 2;
0, 0, 0, 3, 3;
0, 0, 0, 0, 3, 17, 6;
0, 0, 0, 0, 1, 36, 74, 11;
Value is A000055(N) when R=N-1 (last term in each row). (Conjectured by Robert Munafo Dec 28 2009, then proved by Andrew Weimholt and Franklin T. Adams-Watters on Dec 29 2009)
Value is 1 when N=2^R.
Value is 1 when N=(2^R)-1.
Value is R when R>2 and N=(2^R)-2.
Value is A034198(R) when R>2 and N=(2^R)-3.
Conjecture: In general, in each column, the last 2^(R-1) values are the same as the first 2^(N-1) values from the corresponding row of A039754. - Robert Munafo, Dec 30 2009
Value is 0 for all (N,R) for which N is greater than 2^R.
Each term A(N,R) can be computed most efficiently by first enumerating all classifications in A(N-1,R) plus those in A(N-1,R-1), and then adding an additional type and/or partition to each.
LINKS
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Robert Munafo, Jan 21 2010
STATUS
approved