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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-Fran├žois 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.)