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A171682 Number of compositions of n with the smallest part in the first position. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First differences of A097939.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

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

EXAMPLE

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.

MATHEMATICA

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 *)

PROG

(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 */

CROSSREFS

Cf. A079500.

Sequence in context: A002215 A007562 A222855 * A066062 A008929 A164047

Adjacent sequences:  A171679 A171680 A171681 * A171683 A171684 A171685

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Dec 15 2009

EXTENSIONS

Added more terms, Joerg Arndt, Jan 01 2013

STATUS

approved

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Last modified November 21 04:22 EST 2019. Contains 329350 sequences. (Running on oeis4.)