cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Antoine Genitrini

Antoine Genitrini's wiki page.

Antoine Genitrini has authored 2 sequences.

A238887 Cumulated number of leaves in computations trees induced by process trees of size n.

Original entry on oeis.org

0, 1, 3, 12, 63, 418, 3460, 35309, 434879, 6296319, 104601742, 1956519181, 40622160668, 926192254412, 22993939511337, 617288387438399, 17815464892300869, 550018928405927892, 18086444341575141093, 631071177229005331170, 23286118567945953909224
Offset: 0

Author

Antoine Genitrini, Mar 06 2014

Keywords

Crossrefs

Cf. A007852.

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

Original entry on oeis.org

0, 1, 2, 8, 44, 312, 2772, 30024, 385688, 5737232, 96959396, 1834244296, 38390799592, 880648730416, 21968596282440, 592083291341520, 17144219069647920, 530774988154571040, 17495673315094986180, 611738880367145595720, 22614424027640541372360
Offset: 0

Author

Antoine Genitrini, Mar 14 2013

Keywords

Comments

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

References

  • 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.

Crossrefs

Cf. A007852.

Programs

  • Mathematica
    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]

Formula

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