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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. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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: A067856 A160467 A122374 * A010121 A174726 A300239

Adjacent sequences:  A261957 A261958 A261959 * A261961 A261962 A261963

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Sep 06 2015

STATUS

approved

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Last modified January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)