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declare @Table table (id int identity, value int)
insert @Table(value) select 0
insert @Table(value) select 1
insert @Table(value) select 1
insert @Table(value) select 1
insert @Table(value) select 0
insert @Table(value) select 1
insert @Table(value) select 1;

select t.*,
value * power(2, row_number() over (partition by grp order by id) - 1) as generatedsequence
from (select t.*, sum(1 - value) over (order by id) as grp
from @table t
) t
id value grp generatedsequence
1 0 1 0
2 1 1 2
3 1 1 4
4 1 1 8
5 0 2 0
6 1 2 2
7 1 2 4