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A049285
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Restricted partitions.
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6
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0, 0, 0, 0, 1, 1, 2, 4, 7, 13, 24, 43, 78, 141, 253, 455, 818, 1468, 2637, 4734, 8495, 15247, 27361, 49094, 88093, 158063, 283599, 508840, 912956, 1638003, 2938861, 5272795, 9460227, 16973125, 30452380, 54636174, 98025512, 175872397, 315541228, 566127763
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OFFSET
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1,7
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COMMENTS
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Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=5 and p(k) <= 2*p(k+1), see example. [Joerg Arndt, Dec 18 2012]
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REFERENCES
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Minc, H.; A problem in partitions: Enumeration of elements of a given degree in the free commutative entropic cyclic groupoid. Proc. Edinburgh Math. Soc. (2) 11 1958/1959 223-224.
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LINKS
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EXAMPLE
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There are a(10)=13 compositions 10=p(1)+p(2)+...+p(m) with p(1)=5 and p(k) <= 2*p(k+1):
[ 1] [ 5 1 1 1 1 1 ]
[ 2] [ 5 1 1 1 2 ]
[ 3] [ 5 1 1 2 1 ]
[ 4] [ 5 1 2 1 1 ]
[ 5] [ 5 1 2 2 ]
[ 6] [ 5 2 1 1 1 ]
[ 7] [ 5 2 1 2 ]
[ 8] [ 5 2 2 1 ]
[ 9] [ 5 2 3 ]
[10] [ 5 3 1 1 ]
[11] [ 5 3 2 ]
[12] [ 5 4 1 ]
[13] [ 5 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(5, 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}]]]; Table[v[5, n], {n, 1, 40}] (* Jean-François Alcover, Jan 10 2014, translated from 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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STATUS
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approved
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