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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Alois P. Heinz, Rows n = 1..33, flattened 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). Cf. A002865, A135010, A138121, A193173, A194546, A194547, A194549. Sequence in context: A056692 A331600 A039637 * A274009 A069157 A294894 Adjacent sequences:  A194545 A194546 A194547 * A194549 A194550 A194551 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Dec 11 2011 EXTENSIONS More terms from Alois P. Heinz, Dec 19 2011 STATUS approved

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Last modified July 28 19:21 EDT 2021. Contains 346335 sequences. (Running on oeis4.)