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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
0, 1, 2, 5, 10, 37, 154, 1125, 9114, 121957, 1188762, 19782757, 449979290, 7603084389, 147015738266, 4800786586725, 197509352924058, 6557890088131685, 254650888299357082, 7815799643948571749, 315002221645968581530 (list; graph; refs; listen; history; text; internal format)
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: A144636 A320430 A018418 * A155217 A004143 A266162

Adjacent sequences:  A290029 A290030 A290031 * A290033 A290034 A290035

KEYWORD

base,nonn,easy

AUTHOR

Emanuel Landeholm, Jul 18 2017

STATUS

approved

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Last modified February 18 02:57 EST 2020. Contains 332006 sequences. (Running on oeis4.)