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A097979 Total number of largest parts in all compositions of n. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Vincenzo Librandi and Alois P. Heinz, Table of n, a(n) for n = 1..600 (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-Fran├žois 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 A319445 A316318

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

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Last modified August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)