A104462 Convert the binary strings in A101305 to decimal.

0, 2, 20, 328, 10512, 672800, 86118464, 22046326912, 11287719379200, 11558624644301312, 23672063271529088000, 96960771160183144450048, 794302637344220319334797312, 13013854410247705711981319168000, 426437981314996820770203866497040384

Offset: 0

Author

Jorge Coveiro, Apr 23 2005

Keywords

• nonn
• base

Comments

The a(n)-th composition in standard order is (2,3,..,n+1), where the k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. Moreover, the binary indices of a(n) are row n of A193973. Including 1 gives A164894, reverse A246534. - Gus Wiseman, Jun 28 2022

Examples

			From _Gus Wiseman_, Jun 28 2022: (Start)
The terms together with their standard compositions begin:
      0: ()
      2: (2)
     20: (2,3)
    328: (2,3,4)
  10512: (2,3,4,5)
(End)
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..80

Crossrefs

Cf. A101305.

A version for prime indices is A070826.

Cf. A000120, A002110, A029931, A066099, A070939, A164894, A193973, A233564, A246534, A272919, A333218, A333255.

Programs

Maple

convert(10,decimal,binary); convert(10100,decimal,binary); convert(101001000,decimal,binary); convert(10100100010000,decimal,binary); convert(10100100010000100000,decimal,binary);

Mathematica

stcinv[q_]:=Total[2^Accumulate[Reverse[q]]]/2;
Table[stcinv[Range[2,n]],{n,8}] (* Gus Wiseman, Jun 28 2022 *)

Python

def a(n): return 0 if n==0 else int("".join("1"+"0"*(i+1) for i in range(n)), 2)
print([a(n) for n in range(15)]) # Michael S. Branicky, Jun 28 2022

Extensions

a(14) and beyond from Michael S. Branicky, Jun 28 2022