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A006827 Number of partitions of 2n with all subsums different from n.
(Formerly M1351)
6
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

Alois P. Heinz, Table of n, a(n) for n = 1..89

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

N. J. A. Sloane

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 December 13 09:48 EST 2019. Contains 329968 sequences. (Running on oeis4.)