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%I #31 Mar 05 2021 07:49:17
%S 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,
%T 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,
%U 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
%N 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.
%H Alois P. Heinz, <a href="/A194548/b194548.txt">Rows n = 1..33, flattened</a>
%H Tilman Piesk, <a href="/A194602/a194602.txt">Table</a> for A194602, showing the non-one addends.
%e Written as a triangle:
%e 0;
%e 1;
%e 1;
%e 2,1;
%e 2,1;
%e 3,2,2,1;
%e 3,2,2,1;
%e 4,3,3,2,2,2,1;
%e 4,3,3,2,3,2,2,1;
%e 5,4,4,3,3,3,2,3,2,2,2,1;
%e 5,4,4,3,4,3,3,2,3,3,2,2,2,1;
%e 6,5,5,4,4,4,3,4,3,3,3,2,4,3,3,2,3,2,2,2,1;
%e 6,5,5,4,5,4,4,3,4,4,3,3,3,2,4,3,3,3,2,3,2,2,2,1;
%p T:= proc(n) local b, l;
%p b:= proc(n, i, t)
%p if n=0 then l:=l, t
%p elif i>n then
%p else b(n-i, i, t+1); b(n, i+1, t)
%p fi
%p end;
%p if n<2 then 0 else l:= NULL; b(n, 2, 0); l fi
%p end:
%p seq(T(n), n=1..15); # _Alois P. Heinz_, Dec 19 2011
%t T[n_] := Module[{b, l}, b[n0_, i_, t_] :=
%t If[n0==0, l = Append[l, t],
%t If[i>n0, , b[n0-i, i, t+1]; b[n0, i+1, t]]];
%t If[n<2, {0}, l = {}; b[n, 2, 0]; l]];
%t Table[T[n], {n, 1, 15}] // Flatten (* _Jean-François Alcover_, Mar 05 2021, after _Alois P. Heinz_ *)
%Y Row sums give A138135. Row n has length A187219(n).
%Y Cf. A002865, A135010, A138121, A193173, A194546, A194547, A194549.
%K nonn,tabf
%O 1,4
%A _Omar E. Pol_, Dec 11 2011
%E More terms from _Alois P. Heinz_, Dec 19 2011
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