The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A231580 a(n) is the numerator of the probability that n segments of length 2, each placed randomly on a line segment of length 2n, will completely cover the line segment. 4
 1, 2, 7, 34, 638, 4876, 220217, 6885458, 569311642, 7515775348, 197394815194, 78863079581996, 886395722771204, 848070074996694008, 222148423805582000341, 33494470531439170224754, 35665304857619152523926, 280147437461017444466304484 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n=1 the length of the line to cover is equal to 2. There is only one way to cover it with 2-length segment and it will be the full cover. So, the probability is equal to 1. For n=2 the length of the line to cover is equal to 4. Let's start randomly and sequentially to cover it with 2-length segments. The first segment could be placed at 3 position with probability 1/3 in the following ways (xxoo, oxxo, ooxx). The second 2-length segment could be added only in the first and the last cases. So we have the following covers (xxxx, oxxo, xxxx). Thus the probability to find the full cover of 4-length line when it is randomly sequentially filled by 2-length segments is equal to 2/3. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..260 FORMULA Numerator of f(n), where f(0)=1 and f(n) = Sum_{k=0..n-1} f(k)*f(n-k-1)/(2*n-1). - Michael Somos, Mar 01 2014 EXAMPLE 1, 2/3, 7/15, 34/105, 638/2835, 4876/31185, 220217/2027025, 6885458/91216125, 569311642/10854718875, 7515775348/206239658625, 197394815194/7795859096025, ... MAPLE A231580f := proc(n)     option remember;     if n <= 0 then         1;     else         add(procname(k)*procname(n-k-1), k=0..n-1)/(2*n-1) ;     end if; end proc: A231580 := proc(n)     numer(A231580f(n)) ; end proc: seq(A231580(n), n=1..30) ; # R. J. Mathar, Aug 28 2014 MATHEMATICA f[g_List, l_] := f[g, l] = Sum[f[g[[;; n]], l] f[g[[n + 1 ;; ]], l], {n, Length[g] - 1}]/(Total[l + g] - 2 l + 1); f[{_}] = f[{_}, _] = 1; f[ConstantArray[0, #], 2] & /@ Range[2, 20] // Numerator PROG (PARI) f=; for(n=2, 25, f=concat(f, sum(k=1, n-1, (f[k]*f[n-k])) / (2*n-3))); f vector(#f, k, numerator(f[k])) \\ Colin Barker, Jul 24 2014, for sequence shifted by 1 index CROSSREFS Cf. A231634 (denominators). Sequence in context: A222868 A222777 A222891 * A182408 A057298 A058941 Adjacent sequences:  A231577 A231578 A231579 * A231581 A231582 A231583 KEYWORD nonn,frac AUTHOR Philipp O. Tsvetkov, Nov 11 2013 EXTENSIONS Name edited by Jon E. Schoenfield, Nov 13 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)