

A104462


Convert the binary strings in A101305 to decimal.


4



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

0,2


COMMENTS

The a(n)th composition in standard order is (2,3,..,n+1), where the kth composition in standard order (graded reverselexicographic, 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



