The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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: A345973 A329702 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 27 18:55 EST 2023. Contains 359845 sequences. (Running on oeis4.)