This is uncanny indeed! The korvai you have given - even in terms of swaras - is exactly what I came up with too and have been playing in my concerts for several years! It is a very interesting one - I had used it as a teaser to many good artistes. It will appear simple and aesthetic at first level, wrong at the next level until further analysis will prove it right.
Sahana: Excellent! You have almost hit the nail on the head and also expanded upon it. Before I give a detailed answer, I will explain my rationale:
Till date, musicians of both CM and HM (and other systems that I have heard so far) have been dealing with simple arithmatic sequences. Even though much of it is 3rd/4th grade math, there is infinite scope in it and even today, it is a very exciting and rewarding area for me. So, I thought it maybe nice to explore and introduce some other sequences and see if they can be presented aesthetically too and came up with this was a sampler.
Suresh: Sorry, I am not savvy about playing it and uploading it! If I were in India, my disciples would help but I am on a concert tour in Brazil now. I am glad that VK has taken the initiative to try it out and also share it!
Is this intended to be the Fibonacci sequence?
It is intended to be similar to it though not limited to it. If it were simple Fibonacci,
(a) we'd be saddled with 1, 1, 2, 3 etc and
(b) no matter what the tala and gati, the sequence would almost be the same.
My concept is as below:
1. It is desirable to keep it to a single 1, if 1 is our starting point. The next numbers are is 2, 3 (2+1), 5 (3+2), 8 (5+3), etc.
2. The korvai can start with any number, say 3. The sequence would then be 3, 4, 7, 11, 18....
If the korvai starts with 4, the sequence is: 4, 5, 9, 14, 23 ......
This approach will give musical variety to the concept. We could perhaps call it Qualified Fibonacci (QF) sequences.
3. Finally, in large korvais with 2 or more parts, the QF sequences can be just the first part of the korvai and the second part can have conventional strong finishes.
Ex 1: Adi (2 kalais): 3, 4, 7, 11, 18 can be the first part and 3 mishrams can be the final part in say Kamalambam bhajare, Kalyani...
G,, - R,,, - G,R,SND - GRSNDPMGRSN - DN,R,, G | M,D,, MD,N,, - G, R, S | ND - R,S,NDP - D,P,MGR ||(Kamalambam)
Ex 2: Khanda Chapu: 4, 5, 9, 14 = first part and 3x6 is final part.
G,,, - R,,,, - G || , R, S, N, D - R, || ,S,,N,,D,, || P, - GR,SND - RS || ,NDP - DP,MGR||
S,,, - R,,,, - S || , R, G, M, P - R, || ,G,,M,,P,, || D, - SR,GMP - RG || ,MPD - PD,NSR||
G,,, - R,,,, - G || , R, S, N, D - R, || ,S,,N,,D,, || P, - GR,SND - RS || ,NDP - GM,PDN|| (Guruleka)
This concept opens up a whole new world of possibilities in the music world. But only practical singing/playing can show individual korvai's concert-worthiness/limitations.