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A002574
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Restricted partitions.
(Formerly M1070 N0404)
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8
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0, 0, 1, 1, 2, 4, 7, 13, 24, 42, 76, 137, 245, 441, 792, 1420, 2550, 4576, 8209, 14732, 26433, 47424, 85092, 152670, 273914, 491453, 881744, 1581985, 2838333, 5092398, 9136528, 16392311, 29410243, 52766343, 94670652, 169853138, 304741614, 546751437, 980952673, 1759973660
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OFFSET
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1,5
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COMMENTS
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Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=3 and p(k) <= 2*p(k+1), see example. [Joerg Arndt, Dec 18 2012]
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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EXAMPLE
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There are a(8)=13 compositions 8=p(1)+p(2)+...+p(m) with p(1)=3 and p(k) <= 2*p(k+1):
[ 1] [ 3 1 1 1 1 1 ]
[ 2] [ 3 1 1 1 2 ]
[ 3] [ 3 1 1 2 1 ]
[ 4] [ 3 1 2 1 1 ]
[ 5] [ 3 1 2 2 ]
[ 6] [ 3 2 1 1 1 ]
[ 7] [ 3 2 1 2 ]
[ 8] [ 3 2 2 1 ]
[ 9] [ 3 2 3 ]
[10] [ 3 3 1 1 ]
[11] [ 3 3 2 ]
[12] [ 3 4 1 ]
[13] [ 3 5 ]
(End)
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MAPLE
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v := proc(c, d) option remember; local i; if d < 0 or c < 0 then 0 elif d = c then 1 else add(v(i, d-c), i=1..2*c); fi; end; [ seq(v(3, n), n=1..50) ];
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MATHEMATICA
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v[c_, d_] := v[c, d] = If[d < 0 || c < 0, 0, If[d == c, 1, Sum[v[i, d-c], {i, 1, 2*c}]]]; a[n_] := v[3, n]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Apr 05 2013, after Maple *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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