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A171682
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Number of compositions of n with the smallest part in the first position.
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3
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1, 2, 3, 6, 10, 20, 37, 72, 140, 275, 540, 1069, 2118, 4206, 8365, 16659, 33204, 66231, 132179, 263913, 527119, 1053113, 2104428, 4205987, 8407382, 16807410, 33603024, 67187111, 134343790, 268638648, 537198557, 1074270342, 2148336463, 4296343787, 8592156886, 17183457812, 34365534564
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OFFSET
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1,2
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COMMENTS
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First differences of A097939.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..1000
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FORMULA
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G.f. (1-x) * sum(k>=1, x^k/(1-x-x^k) ). [Joerg Arndt, Jan 01 2013]
a(n) ~ 2^(n-2). - Vaclav Kotesovec, Sep 10 2014
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EXAMPLE
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The a(6)=20 such compositions of 6 are
[ 1] [ 1 1 1 1 1 1 ]
[ 2] [ 1 1 1 1 2 ]
[ 3] [ 1 1 1 2 1 ]
[ 4] [ 1 1 1 3 ]
[ 5] [ 1 1 2 1 1 ]
[ 6] [ 1 1 2 2 ]
[ 7] [ 1 1 3 1 ]
[ 8] [ 1 1 4 ]
[ 9] [ 1 2 1 1 1 ]
[10] [ 1 2 1 2 ]
[11] [ 1 2 2 1 ]
[12] [ 1 2 3 ]
[13] [ 1 3 1 1 ]
[14] [ 1 3 2 ]
[15] [ 1 4 1 ]
[16] [ 1 5 ]
[17] [ 2 2 2 ]
[18] [ 2 4 ]
[19] [ 3 3 ]
[20] [ 6 ]
- Joerg Arndt, Jan 01 2013.
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MATHEMATICA
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nn=37; Drop[CoefficientList[Series[Sum[x^i/(1-x^i/(1-x)), {i, 1, nn}], {x, 0, nn}], x], 1] (* Geoffrey Critzer, Mar 12 2013 *)
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PROG
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(PARI)
N=66; x='x+O('x^N);
gf= (1-x) * sum(k=1, N, x^k/(1-x-x^k) );
Vec(gf)
/* Joerg Arndt, Jan 01 2013 */
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CROSSREFS
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Cf. A079500.
Sequence in context: A345973 A329702 A222855 * A066062 A008929 A164047
Adjacent sequences: A171679 A171680 A171681 * A171683 A171684 A171685
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic, Dec 15 2009
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EXTENSIONS
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Added more terms, Joerg Arndt, Jan 01 2013
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STATUS
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approved
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