HeikinAshi: another candle

motivated by email from Ken G.
We've talked about candlesticks before.
Ths "usual" candlestick generates a neat chart, using only today's Open, High, Low and Close ... but ignores any previous data.
>Previous? Like last week's High, Low ... ?
Actually, I want to talk about the HeikinAshi candles which use one piece of info from yesterday's stock numbers: the Close.
It also uses some of its own numbers from yesterday.
The HA candles generate a different set of High, Low, Open and Close ... like so:
 
If O(n), H(n), L(n), C(n) are today's stock Open, High, Low and Close
and
xO(n), xH(n), xL(n), xC(n) are today's HeikinAshi Open, High, Low and Close
then
xC(n) = ( O(n) +H(n) +L(n) +C(n) )/4  the average of today's stock numbers 
xO(n) = ( xO(n1) + C(n1) ) / 2  the average of yesterday's HA Open and yesterday's stock Close 
xH(n) = Max[ H(n), xO(n), xC(n) ]  the Maximum of today's stock High and today's HA Open and Close 
xL(n) = Min[ L(n), xO(n), xC(n) ]  the Minimum of today's stock Low and today's HA Open and Close 

For example, in the Doji, the Open and Close are equal (or very nearly so).
You do the HeikinAshi ... and it's gone.
Indeed, in order to see a HeikinAshi Doji, we'd need xO(n) = xC(n):
( xO(n1) + C(n1) ) / 2 = ( O(n) +H(n) +L(n) +C(n) )/4
which is unlikely. In fact, I played with several stocks and found no Dojis so I figure that ...
>You played ... with what?
A spreadsheet. It's just a modification of an earlier spreadsheet, but you can pick reg'lar or HeikinAshi and ...
>Can you just show the spreadsheet?
 
>It's guaranteed to work?
Nope.
