This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A079501 Number of compositions of the integer n with strictly smallest part in the first position. 8
 1, 1, 2, 2, 4, 5, 8, 12, 19, 28, 45, 70, 110, 173, 275, 436, 695, 1107, 1769, 2831, 4537, 7276, 11683, 18774, 30194, 48592, 78247, 126062, 203192, 327645, 528518, 852815, 1376491, 2222294, 3588628, 5796196, 9363458, 15128631, 24447014, 39510108 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also number of compositions of n such that the first part is divisible by the number of parts . [Vladeta Jovovic, Dec 02 2009] REFERENCES Arnold Knopfmacher and Neville Robbins, Compositions with parts constrained by the leading summand, Ars Combin. 76 (2005), 287-295. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 FORMULA G.f.: sum(k>=1, (1-z)*z^k/(1-z-z^(k+1)) ). Also sum(k>=1, z^(2*k-1)/((1-z^k)*(1-z)^(k-1)) ), cf. A105039. - Vladeta Jovovic, Apr 05 2005 a(n) ~ 1/sqrt(5) * ((1+sqrt(5))/2)^(n-2). - Vaclav Kotesovec, May 01 2014 EXAMPLE The a(9)=19 such compositions of 9 are [ 1]  [ 1 2 2 2 2 ] [ 2]  [ 1 2 2 4 ] [ 3]  [ 1 2 3 3 ] [ 4]  [ 1 2 4 2 ] [ 5]  [ 1 2 6 ] [ 6]  [ 1 3 2 3 ] [ 7]  [ 1 3 3 2 ] [ 8]  [ 1 3 5 ] [ 9]  [ 1 4 2 2 ] [10]  [ 1 4 4 ] [11]  [ 1 5 3 ] [12]  [ 1 6 2 ] [13]  [ 1 8 ] [14]  [ 2 3 4 ] [15]  [ 2 4 3 ] [16]  [ 2 7 ] [17]  [ 3 6 ] [18]  [ 4 5 ] [19]  [ 9 ] - Joerg Arndt, Jan 01 2013 MAPLE b:= proc(n, s) option remember; `if`(n=0, 1, add(       `if`(n-j>0 and n-j<=s, 0, b(n-j, s)), j=s+1..n))     end: a:= n-> 1 +add(b(n-j, j), j=1..n/2): seq(a(n), n=1..60);  # Alois P. Heinz, Apr 29 2014 MATHEMATICA b[n_, s_] := b[n, s] = If[n == 0, 1, Sum[ If[n - j > 0 && n - j <= s, 0, b[n - j, s]], {j, s + 1, n}]]; a[n_] := 1 + Sum[b[n - j, j], {j, 1, n/2}]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Jan 16 2015, after Alois P. Heinz *) CROSSREFS Cf. A168655, A168656, A168657. [From Vladeta Jovovic, Dec 02 2009] Sequence in context: A172128 A274154 A274153 * A093335 A093333 A116085 Adjacent sequences:  A079498 A079499 A079500 * A079502 A079503 A079504 KEYWORD nonn AUTHOR Arnold Knopfmacher, Jan 21 2003 EXTENSIONS More terms from Benoit Cloitre, Jan 21 2003 STATUS approved

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

Last modified December 19 08:25 EST 2018. Contains 318245 sequences. (Running on oeis4.)