A293308 Number of permutations of zero-one words with A056576(n)-n zeros and n-1 ones.

1, 2, 3, 10, 15, 56, 210, 330, 1287, 2002, 8008, 31824, 50388, 203490, 319770, 1307504, 2042975, 8436285, 34597290, 54627300, 225792840, 354817320, 1476337800, 6107086800, 9669554100, 40225345056, 63432274896, 265182149218, 416714805914, 1749695026860

Offset: 1

Author

Frank Ellermann, Oct 05 2017

Keywords

• nonn

Examples

			a(4) = 5! / ( 2! * 3! ) = 5*4/2 = 10.
From _Mike Winkler_, Oct 30 2017: (Start)
The next table shows the output using the PARI function NextPermutation(a), (cf. PROG)
[0, 0, 1, 1, 1] 1
[0, 1, 0, 1, 1] 2
[0, 1, 1, 0, 1] 3
[0, 1, 1, 1, 0] 4
[1, 0, 0, 1, 1] 5
[1, 0, 1, 0, 1] 6
[1, 0, 1, 1, 0] 7
[1, 1, 0, 0, 1] 8
[1, 1, 0, 1, 0] 9
[1, 1, 1, 0, 0] 10
(End)
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..2211
• Mike Winkler, The algorithmic structure of the finite stopping time behavior of the 3x + 1 function, arXiv:1709.03385 [math.GM], Sep 2017. [see (17) on p. 9]

Crossrefs

Cf. A056576, A100982.

Programs

Mathematica

Table[(# - 1)!/((# - n)!*(n - 1)!) &@ Floor[n Log[2, 3]], {n, 30}] (* Michael De Vlieger, Oct 06 2017 *)

PARI

/* method used in the linked paper arXiv:1709.03385 */
NextPermutation(a) = {i=#a-1; while(!(i<1 || a[i]a[i]), k--); t=a[k]; a[k]=a[i]; a[i]=t; for(k=i+1, (#a+i)/2, t=a[k]; a[k]=a[#a+1+i-k]; a[#a+1+i-k]=t); return(a)}
  /* example for n = 4 */
  {j=1; a=[0, 0, 1, 1, 1]; until(a==0, print(a" "j); j++; a=NextPermutation(a))} \\ Mike Winkler, Oct 30 2017

Formula

a(n) = ( A056576(n) - 1 )! / ( ( A056576(n) - n )! * ( n - 1)! )