%I #18 Jan 22 2013 18:37:44

%S 2,4,6,9,13,23,29,43,51,60,80,91,103,116,144,159,175,192,210,248,268,

%T 289,311,334,382,407,433,460,516,545,605,636,668,701,769,804,840,914,

%U 952,991,1031,1113,1155,1198,1286,1331,1377,1424,1520,1569,1669,1720,1824,1877,1931,1986,2098,2155,2271,2330,2390,2512,2574,2637,2701,2831,2897,3031,3099,3168,3238

%N Length of n-th run of A205600(n).

%H Benoit Cloitre, <a href="/A205883/a205883.png">Plot of a(n)/n^2</a>

%F a(n)=2+sum(k=1,n,A205600(k)*(k-1)). It seems that a(n)=c*n^2+smaller terms with c=0.64...(see graphic provided in the link)

%o (PARI) /* program to get the first 100 terms: */ v=[1,2];L=[2];for(n=2,100,v=if(v[n]-2,concat(v,vector(n-1,i,v[i])),concat(concat(v,vector(n-1,i,v[i])),vector(n-1,i,v[i])));L=concat(L,[length(v)]));a(n)=L[n]

%K nonn

%O 1,1

%A _Benoit Cloitre_, Jan 10 2013