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A112956
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a(n) = number of ways the set {1,2,...,n} can be split into proper subsets with equal sums.
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1
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0, 0, 1, 1, 1, 1, 5, 11, 10, 1, 79, 165, 1, 664, 2917, 3308, 9295, 23729, 31874, 301029, 422896, 1, 13716866, 71504979, 100664384, 54148590, 880696661, 498017758, 27450476786, 111911522818, 179459955553, 2144502175213, 59115423982
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| For n=7 we have splittings 761/5432, 752/6431, 743/6521, 7421/653 and 7/61/52/43 so a(7)=5.
a(n) = 1 <=> n*(n+1)/2 is product of two primes. - Alois P. Heinz, Sep 03 2009
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FORMULA
| a(n) = A035470(n) - 1. - Frank Adams-Watters, Jun 02 2006
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MAPLE
| with (numtheory): b:= proc() option remember; local i, j, t; `if` (args[1]=0, `if` (nargs=2, 1, b(args[t] $t=2..nargs)), add (`if` (args[j] -args[nargs] <0, 0, b(sort ([seq (args[i] -`if` (i=j, args[nargs], 0), i=1..nargs-1)])[], args[nargs]-1)), j=1..nargs-1)) end: a:= proc(n) local i, m, x; m:= n*(n+1)/2; add (b(i$(m/i), n)/(m/i)!, i=[select (x-> x>=n, divisors(m) minus {m})[]]) end: seq (a(n), n=1..25); # Alois P. Heinz, Sep 03 2009
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CROSSREFS
| Cf. A035470.
Cf. A164977, A164978. - Alois P. Heinz, Sep 03 2009
Sequence in context: A113964 A075261 A185201 * A157801 A061768 A205673
Adjacent sequences: A112953 A112954 A112955 * A112957 A112958 A112959
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KEYWORD
| nonn
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AUTHOR
| Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 07 2005
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EXTENSIONS
| More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 02 2006
a(19) - a(33) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 03 2009
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