A097979 Total number of largest parts in all compositions of n.

1, 3, 6, 12, 23, 46, 91, 183, 367, 737, 1478, 2962, 5928, 11858, 23707, 47384, 94698, 189260, 378277, 756160, 1511730, 3022672, 6044472, 12088395, 24177600, 48359695, 96732370, 193495606, 387057584, 774248858, 1548754115, 3097980230, 6196797193, 12395022288

Offset

1,2

Comments

Also number of compositions of n+1 with unique largest part. - Vladeta Jovovic, Apr 03 2005

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 200 terms from Vincenzo Librandi)

Formula

G.f.: (1-x)^2 * Sum_{k>=1} x^k/(1-2*x+x^(k+1))^2.

a(n) ~ 2^(n-1)/log(2). - Vaclav Kotesovec, Apr 30 2014

Mathematica

nn=32; Drop[CoefficientList[Series[Sum[x^j/(1 - (x - x^(j + 1))/(1 - x))^2, {j, 1, nn}], {x, 0, nn}], x], 1] (* Geoffrey Critzer, Mar 31 2014 *)
b[n_, p_, i_] := b[n, p, i] = If[n == 0, p!, If[i<1, 0, Sum[b[n-i*j, p+j, i-1]/j!, {j, 0, n/i}]]]; a[n_, k_] := Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]; a[0, 0] = 1; a[_, 0] = 0; a[n_] := a[n+1, 1]; Table[a[n], {n, 1, 32}] (* Jean-François Alcover, Feb 10 2015, after A238341 *)

Prog

(PARI) { b(t)=local(r); sum(k=1, t, forstep(s=t%k, t-k, k, u=(t-k-s)\k; r+=binomial(-2, s)*(-2)^(s-u)*binomial(s, u))); r }
{ a(n)=b(n)-2*b(n-1)+b(n-2) } \\ Max Alekseyev, Apr 16 2005

Crossrefs

Cf. A097941, A046746.

Column k=1 of A238341.

Sequence in context: A285262 A024505 A005256 * A215983 A339107 A319445

Adjacent sequences: A097976 A097977 A097978 * A097980 A097981 A097982

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 07 2004

Extensions

More terms from Max Alekseyev, Apr 16 2005

Status

approved