On your TI calculator,
Press STAT
Press ENTER
Under L1, store 1, 2, 3, 4
Under  L2, store 16, 28, 42, 56
Press STAT
Press the right arrow key to highlight CALC
Press 6 for 6:CubicReg
See this screen:

     CubicReg
Xlist:L1
Xlist:L2
Store RegEQ:
Calculate

Press down arrow key 4 times to highlight Calculate

Press ENTER

See this screen:
    
    CubicReg
y=ax3+bx2+cx+d
a=-0.333333333
b=3
c=5.3333333333
d=8
R2=1

Interpret -0.333333333 as -1/3
interpret  5.333333333 as 5 1/3 and then as 16/3

So the equation is this, using n for x:



Checking:

for n=1








for n=2








for n=3








for n=4








For more terms, calculate as above:

16,28,42,56,68,76,78,72,56,28,-14,-72,-148,...

Edwin