A290032 a(0)=0; for n > 0, a(n) is the sum of the partial sums of binary digits of a(n-1) + 1, starting from the least significant digit, and given weights 1, 2, 2^2, etc.

0, 1, 2, 5, 10, 37, 154, 1125, 9114, 121957, 1188762, 19782757, 449979290, 7603084389, 147015738266, 4800786586725, 197509352924058, 6557890088131685, 254650888299357082, 7815799643948571749, 315002221645968581530

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Example

a(4) is computed as follows: a(3) + 1 = 6 = 110_2; the partial sums of digits and their weights are (0,1), (0+1,2), and (0+1+1,4), so the sum of partial sums is 0*1 + 1*2 + 2*4 = 10.

Mathematica

PartialSums = Function[Accumulate[Reverse[IntegerDigits[#, 2]]]]
NestList[Total[# Power[2, Range[0, Length[#] - 1]]] &[PartialSums[1 + #]] &, 0, 20]

Crossrefs

Sequence in context: A320430 A018418 A363429 * A155217 A004143 A266162

Adjacent sequences: A290029 A290030 A290031 * A290033 A290034 A290035

Keyword

base,nonn,easy

Author

Emanuel Landeholm, Jul 18 2017

Status

approved