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A006827
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Number of partitions of 2n with all subsums different from n.
(Formerly M1351)
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7
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1, 2, 5, 8, 17, 24, 46, 64, 107, 147, 242, 302, 488, 629, 922, 1172, 1745, 2108, 3104, 3737, 5232, 6419, 8988, 10390, 14552, 17292, 23160, 27206, 36975, 41945, 57058, 65291, 85895, 99384, 130443, 145283, 193554, 218947, 281860, 316326, 413322, 454229, 594048
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OFFSET
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1,2
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REFERENCES
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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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Fausto A. C. Cariboni, Table of n, a(n) for n = 1..140 (terms 1..89 from Alois P. Heinz)
P. Erdős, J. L. Nicolas and A. Sárközy, On the number of partitions of n without a given subsum (I), Discrete Math., 75 (1989), 155-166 = Annals Discrete Math. Vol. 43, Graph Theory and Combinatorics 1988, ed. B. Bollobas.
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FORMULA
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a(n) = A000041(2*n) - A002219(n).
a(n) = A046663(2*n,n).
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MAPLE
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b:= proc(n, i, s) option remember;
`if`(0 in s or n in s, 0, `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, s)+
`if`(i<=n, b(n-i, i, select(y-> 0<=y and y<=n-i,
map(x-> [x, x-i][], s))), 0))))
end:
a:= n-> b(2*n, 2*n, {n}):
seq(a(n), n=1..25); # Alois P. Heinz, Jul 10 2012
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MATHEMATICA
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b[n_, i_, s_] := b[n, i, s] = If[MemberQ[s, 0 | n], 0, If[n == 0, 1, If[i < 1, 0, b[n, i-1, s] + If[i <= n, b[n-i, i, Select[Flatten[Transpose[{s, s-i}]], 0 <= # <= n-i &]], 0]]]]; a[n_] := b[2*n, 2*n, {n}]; Table[Print[an = a[n]]; an, {n, 1, 25}] (* Jean-François Alcover, Nov 12 2013, after Alois P. Heinz *)
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CROSSREFS
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Cf. A046663.
Sequence in context: A103041 A216307 A176223 * A193992 A112346 A062318
Adjacent sequences: A006824 A006825 A006826 * A006828 A006829 A006830
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Don Reble, Nov 03 2001
More terms from Alois P. Heinz, Jul 10 2012
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STATUS
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approved
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