n= 1,2,3,4,5,6,...n c= 1,3,6,10,,15,21,...n(n+1)/2 m= 0,1,2,4,6,9...
Am trying to find out if there a formulae that could be generated to fill in the sequence for m. I know the pattern as follows: m1+1=m2 => 0+1=1 m2+1=m3 => 1+1=2 m3+2=m4 => 2+2=4 m4+2=m5 => 4+2=6 m5+3=m6 => 6+3=9
The ratio keeps adding by 1 after every two values. any help towards figuring out a formula would be much appreciated.
Found this on the encyclopedia of the integer sequences
The formula is the following:
$$a_n=\sum_{j=1}^{n} \left\lfloor \sum_{k=1}^{j}k\sqrt3-\lfloor k\sqrt3\rfloor\right \rfloor $$
I wrote a small script on python:
Try it here