Question 1167274
<pre>

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:

{{{a[n]=expr(-1/3)n^3+3n^2+expr(16/3)n+8}}}

Checking:

for n=1

{{{a[1]=expr(-1/3)(1)^3+3(1)^2+expr(16/3)(1)+8}}}
{{{a[1]=expr(-1/3)(1)+3(1)+expr(16/3)+8}}}
{{{a[1]=-1/3+3+16/3+8}}}
{{{a[1]=-1/3+9/3+16/3+24/3}}}
{{{a[1]=48/3}}}
{{{a[1]=16}}}

for n=2

{{{a[2]=expr(-1/3)(2)^3+3(2)^2+expr(16/3)(2)+8}}}
{{{a[2]=expr(-1/3)(8)+3(4)+expr(32/3)+8}}}
{{{a[2]=-8/3+12+32/3+8}}}
{{{a[2]=-8/3+36/3+32/3+24/3}}}
{{{a[2]=84/3}}}
{{{a[2]=28}}}

for n=3

{{{a[3]=expr(-1/3)(3)^3+3(3)^2+expr(16/3)(3)+8}}}
{{{a[3]=expr(-1/3)(27)+3(9)+expr(48/3)+8}}}
{{{a[3]=-27/3+27+48/3+8}}}
{{{a[3]=-27/3+81/3+48/3+24/3}}}
{{{a[3]=126/3}}}
{{{a[3]=42}}}

for n=4

{{{a[4]=expr(-1/3)(4)^3+3(4)^2+expr(16/3)(4)+8}}}
{{{a[4]=expr(-1/3)(64)+3(16)+expr(64/3)+8}}}
{{{a[4]=-64/3+48+64/3+8}}}
{{{a[4]=-64/3+144/3+64/3+24/3}}}
{{{a[4]=168/3}}}
{{{a[4]=56}}}

For more terms, calculate as above:

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

Edwin</pre>