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A097979 Total number of largest parts in all compositions of n. 10
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
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-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
Column k=1 of A238341.
Sequence in context: A285262 A024505 A005256 * A215983 A339107 A319445
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 March 19 06:32 EDT 2024. Contains 370953 sequences. (Running on oeis4.)