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

0,2

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

Links

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

Example

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)

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 *)

Prog

(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

Crossrefs

Cf. A101305.

A version for prime indices is A070826.

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

Sequence in context: A294454 A322729 A304861 * A352601 A060164 A267827

Adjacent sequences: A104459 A104460 A104461 * A104463 A104464 A104465

Keyword

nonn,base

Author

Jorge Coveiro, Apr 23 2005

Extensions

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

Status

approved