cp's OEIS Frontend

A216234 Cumulated number of increasing admissible cuts of rooted plane trees of size n.

%I A216234 #20 Jan 31 2015 17:01:10
%S A216234 0,1,2,8,44,312,2772,30024,385688,5737232,96959396,1834244296,
%T A216234 38390799592,880648730416,21968596282440,592083291341520,
%U A216234 17144219069647920,530774988154571040,17495673315094986180,611738880367145595720,22614424027640541372360
%N A216234 Cumulated number of increasing admissible cuts of rooted plane trees of size n.
%C A216234 In concurrency theory, a(n) is also the cumulated sizes of computation trees induced by interleaved concurrent processes of size n.
%D A216234 O. Bodini, A. Genitrini and F. Peschanski. Enumeration and Random Generation of Concurrent Computations. In proc. 23rd International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA'12), Discrete Mathematics and Theoretical Computer Science, pp 83-96, 2012.
%H A216234 O. Bodini, A. Genitrini, F. Peschanski, <a href="http://arxiv.org/abs/1407.1873">A Quantitative Study of Pure Parallel Processes</a>, arXiv preprint arXiv:1407.1873, 2014
%F A216234 P-recurrence: (16*n-64*n^3)*a(n)+(12+72*n+112*n^2+32*n^3)*a(n+1)+(-26-62*n-4*n^3-36*n^2)*a(n+2)+(5+7*n+2*n^2)*a(n+3) = 0; a(0)=0; a(1)=1; a(2)=2.
%F A216234 a(n) ~ 2^(n-1/2) * n^(n-1) / exp(n-1). - _Vaclav Kotesovec_, Mar 08 2014
%t A216234 Flatten[{0,RecurrenceTable[{-16*(-3+n)*(-7+2*n)*(-5+2*n)*a[-3+n]+4*(-5+2*n)*(3-12*n+4*n^2)*a[-2+n]-2*(28-23*n+2*n^3)*a[-1+n]+(-2+n)*(-1+2*n)*a[n]==0,a[1]==1,a[2]==2,a[3]==8},a,{n,1,20}]}] (* _Vaclav Kotesovec_, Mar 08 2014 *)
%o A216234 (Python)
%o A216234 def a(n):
%o A216234    if n < 3:
%o A216234       return n
%o A216234    l = [0,1,2]
%o A216234    for i in range(n-2):
%o A216234       l[i%3] = ( (16*i-64*i**3)*l[i%3]+(12+72*i+112*i**2+32*i**3)*l[(i+1)%3]+(-26-62*i-4*i**3-36*i**2)*l[(i+2)%3] ) / (-5-7*i-2*i**2)
%o A216234    return l[i%3]
%Y A216234 Cf. A007852.
%K A216234 nonn
%O A216234 0,3
%A A216234 _Antoine Genitrini_, Mar 14 2013