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A261960
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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.
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6
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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
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OFFSET
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0,6
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LINKS
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EXAMPLE
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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, ...
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MAPLE
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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);
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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