0,3

In concurrency theory, a(n) is also the cumulated sizes of computation trees induced by interleaved concurrent processes of size n.

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.

O. Bodini, A. Genitrini, F. Peschanski, A Quantitative Study of Pure Parallel Processes, arXiv preprint arXiv:1407.1873, 2014

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.

a(n) ~ 2^(n-1/2) * n^(n-1) / exp(n-1). - Vaclav Kotesovec, Mar 08 2014

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 *)

(Python)

def a(n):

if n < 3:

return n

l = [0, 1, 2]

for i in range(n-2):

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)

return l[i%3]

Cf. A007852.

Sequence in context: A212913 A321628 A005363 * A123307 A293905 A244430

Adjacent sequences: A216231 A216232 A216233 * A216235 A216236 A216237

Antoine Genitrini, Mar 14 2013

approved