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A194548
Triangle read by rows: T(n,k) = number of parts in the k-th partition of n that does not contain 1 as a part, with partitions in lexicographic order.
9
0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 3, 3, 2, 3, 2, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 3, 3, 2, 2, 2, 1, 6, 5, 5, 4, 4, 4, 3, 4, 3, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 2, 1, 6, 5, 5, 4, 5, 4, 4, 3, 4, 4, 3, 3, 3, 2, 4, 3, 3, 3, 2, 3, 2, 2, 2, 1
OFFSET
1,4
LINKS
Tilman Piesk, Table for A194602, showing the non-one addends.
EXAMPLE
Written as a triangle:
0;
1;
1;
2,1;
2,1;
3,2,2,1;
3,2,2,1;
4,3,3,2,2,2,1;
4,3,3,2,3,2,2,1;
5,4,4,3,3,3,2,3,2,2,2,1;
5,4,4,3,4,3,3,2,3,3,2,2,2,1;
6,5,5,4,4,4,3,4,3,3,3,2,4,3,3,2,3,2,2,2,1;
6,5,5,4,5,4,4,3,4,4,3,3,3,2,4,3,3,3,2,3,2,2,2,1;
MAPLE
T:= proc(n) local b, l;
b:= proc(n, i, t)
if n=0 then l:=l, t
elif i>n then
else b(n-i, i, t+1); b(n, i+1, t)
fi
end;
if n<2 then 0 else l:= NULL; b(n, 2, 0); l fi
end:
seq(T(n), n=1..15); # Alois P. Heinz, Dec 19 2011
MATHEMATICA
T[n_] := Module[{b, l}, b[n0_, i_, t_] :=
If[n0==0, l = Append[l, t],
If[i>n0, , b[n0-i, i, t+1]; b[n0, i+1, t]]];
If[n<2, {0}, l = {}; b[n, 2, 0]; l]];
Table[T[n], {n, 1, 15}] // Flatten (* Jean-François Alcover, Mar 05 2021, after Alois P. Heinz *)
CROSSREFS
Row sums give A138135. Row n has length A187219(n).
Sequence in context: A056692 A331600 A039637 * A274009 A069157 A294894
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Dec 11 2011
EXTENSIONS
More terms from Alois P. Heinz, Dec 19 2011
STATUS
approved