Question 942092
If a general formula is to be a polynomial,
you can find it by calculating differences between consecutive terms,
and then differences between the already found differences.
The second term is {{{3-6=-3}}} more than the one before (the first term).
THat means to get to the second term you add {{{-3}}} to the term before.
The third term is {{{(-4)-3=-7}}} more than the one before (the second term).
The next difference is {{{-14-(-4)=-14+4=-10}}} .
The next difference is {{{-26-(-14)=-26+14=-12}}}.
The next difference is {{{-39-(-26)=-39+26=-13}}}.
The next difference is {{{-52-(-39)=-52+39=-13}}} .
{{{matrix(7,2,
6," ",
3,-3,
-4,-7,
-14,-10,
-26,-12,
-39,-13,
-52,-13)}}}
The differences form the sequence
{{{-3}}} , {{{-10}}} , {{{-12}}} , {{{-13}}} , {{{-13}}} .
Their differences are
{{{-4}}} , {{{-3}}} , {{{-2}}} , {{{-1}}} , and {{{0}}} :
{{{-7-(-3)=-7+3=-4}}}
{{{-10-(-7)=-10+7=-3}}}
{{{-12-(-10)=-12+10=-2}}} 
{{{-13-(-12)=-13+12=-1}}}
{{{-13-(-13)=-13+13=0}}}
{{{matrix(7,3,
6," "," ",
3,-3," ",
-4,-7,-4,
-14,-10,-3,
-26,-12,-2,
-39,-13,-1,
-52,-13,0)}}}
If we calculate the differences of differences of differences,
we find that the result is always the same.
The differences of differences increase by 1 each time.
The next difference of differences should be {{{red(1)}}} : {{{matrix(8,4,
6," "," "," ",
3,-3," "," ",
-4,-7,-4," ",
-14,-10,-3,1,
-26,-12,-2,1,
-39,-13,-1,1,
-52,-13,0,1,
"?","?",red(1),1)}}}
That means the next difference should be
{{{-13+1=-12}}} : {{{matrix(8,3,
6," "," ",
3,-3," ",
-4,-7,-4,
-14,-10,-3,
-26,-12,-2,
-39,-13,-1,
-52,-13,0,
"?",red(12),red(1))}}}
and that would make the next number
{{{-52+(-12)=highlight(-64)}}} : {{{matrix(8,3,
6," "," ",
3,-3," ",
-4,-7,-4,
-14,-10,-3,
-26,-12,-2,
-39,-13,-1,
-52,-13,0,
highlight(red(-64)),red(12),red(1))}}}