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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
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.
Sequence in context: A294454 A322729 A304861 * A352601 A060164 A267827
KEYWORD
nonn,base
AUTHOR
Jorge Coveiro, Apr 23 2005
EXTENSIONS
a(14) and beyond from Michael S. Branicky, Jun 28 2022
STATUS
approved