Indices of Triangular numbers

[Creighton Dement]

Dear Seqfans, 

I am currently working on the page 
http://www.crowdog.de/SeqContext/CubeButterfly.html

I noticed that the transform of the sequence (1, -1, 1, -1, )  -  the
sequence  (0, 1, 5, 20, 76, 285, 1065, ) - as discussed in the first
text box is listed under 
http://www.research.att.com/projects/OEIS?Anum=A001834 along with the
comment:

Indices m of triangular numbers T(m) which are one-third of another
triangular number: 3*T(m)=T(k); the k's are given by A001571. - Bruce
Corrigan (scentman(AT)myfamily.com), Oct 31 2002

My question is if the transform of the sequence (-1, 1, -1, 1) under the
same conditions - the sequence  (0, 1, 3, 10, 36, 133, 495, 1846) -  
might also be related to the triangular numbers; perhaps similarly
giving indices of triangular numbers which are somehow of interest.. 

If it gave indices of triangular numbers, the sequence would
start off (0, 1, 6, 55, 666), assuming counting is to begin from the
initial term.of A000217.

Sincerely, 
Creighton 
 

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