A261960 Number A(n,k) of compositions of n such that no part equals any of its k immediate predecessors; square array A(n,k), n>=0, k>=0, read by antidiagonals.

1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 3, 8, 1, 1, 1, 3, 4, 16, 1, 1, 1, 3, 3, 7, 32, 1, 1, 1, 3, 3, 5, 14, 64, 1, 1, 1, 3, 3, 5, 11, 23, 128, 1, 1, 1, 3, 3, 5, 11, 15, 39, 256, 1, 1, 1, 3, 3, 5, 11, 13, 23, 71, 512, 1, 1, 1, 3, 3, 5, 11, 13, 19, 37, 124, 1024

Offset

0,6

Links

Alois P. Heinz, Antidiagonals n = 0..50, flattened

Example

Square array A(n,k) begins:
:  1,  1,  1,  1,  1,  1,  1, ...
:  1,  1,  1,  1,  1,  1,  1, ...
:  2,  1,  1,  1,  1,  1,  1, ...
:  4,  3,  3,  3,  3,  3,  3, ...
:  8,  4,  3,  3,  3,  3,  3, ...
: 16,  7,  5,  5,  5,  5,  5, ...
: 32, 14, 11, 11, 11, 11, 11, ...

Maple

b:= proc(n, l) option remember;
      `if`(n=0, 1, add(`if`(j in l, 0, b(n-j,
      `if`(l=[], [], [subsop(1=NULL, l)[], j]))), j=1..n))
    end:
A:= (n, k)-> b(n, [0$min(n, k)]):
seq(seq(A(n, d-n), n=0..d), d=0..12);

Mathematica

b[n_, l_] := b[n, l] = If[n==0, 1, Sum[If[MemberQ[l, j], 0, b[n-j, If[l == {}, {}, Append[Rest[l], j]]]], {j, 1, n}]]; A[n_, k_] := b[n, Array[0&, Min[n, k]]]; Table[A[n, d-n], {d, 0, 12}, {n, 0, d}] // Flatten (* Jean-François Alcover, Feb 08 2017, translated from Maple *)

Crossrefs

Columns k=0-2 give: A011782, A003242, A261962.

Main diagonal gives A032020.

Cf. A261959, A261981.

Sequence in context: A345000 A352894 A122374 * A010121 A174726 A300239

Adjacent sequences: A261957 A261958 A261959 * A261961 A261962 A261963

Keyword

nonn,tabl

Author

Alois P. Heinz, Sep 06 2015

Status

approved