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 A006827 Number of partitions of 2n with all subsums different from n. (Formerly M1351) 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS 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. FORMULA a(n) = A000041(2*n) - A002219(n). a(n) = A046663(2*n,n). MAPLE 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 MATHEMATICA 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 *) CROSSREFS Cf. A046663. Sequence in context: A103041 A216307 A176223 * A193992 A112346 A062318 Adjacent sequences: A006824 A006825 A006826 * A006828 A006829 A006830 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from Don Reble, Nov 03 2001 More terms from Alois P. Heinz, Jul 10 2012 STATUS approved

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Last modified March 23 04:41 EDT 2023. Contains 361434 sequences. (Running on oeis4.)