A290032 - OEIS

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.

%I #21 Aug 31 2017 14:20:22

%S 0,1,2,5,10,37,154,1125,9114,121957,1188762,19782757,449979290,

%T 7603084389,147015738266,4800786586725,197509352924058,

%U 6557890088131685,254650888299357082,7815799643948571749,315002221645968581530

%N 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.

%e 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.

%t PartialSums = Function[Accumulate[Reverse[IntegerDigits[#, 2]]]]

%t NestList[Total[# Power[2, Range[0, Length[#] - 1]]] &[PartialSums[1 + #]] &, 0, 20]

%K base,nonn,easy

%O 0,3

%A _Emanuel Landeholm_, Jul 18 2017