Question 891573
You are given the first 3 terms as {{{system(z[1]=0,z[2]=1,z[3]=2)}}}
and for the other terms you are given a recursive formula to calculate a term from the 3 previous terms:
for {{{m>=4}}} , {{{z[m]=z[(m-1)] + 2z[(m-2)]+ 3z[(m-3)]}}} .
Using that formula:
{{{z[4]=z[(4-1)]+2z[(4-2)]+3z[(4-3)]=z[3]+2z[2]+ 3z[1]=2+2*1+3*0=2+2=highlight(4)}}} ,
{{{z[5]=z[(5-1)]+2z[(5-2)]+3z[(5-3)] =z[4]+2z[3]+3z[2]=4+2*2+3*1=4+4+3=highlight(11)}}} , and
{{{z[6]=z[(6-1)]+2z[(6-2)]+3z[(6-3)]
=z[5]+2z[4]+3z[3]=11+2*4+3*2=11+8+6=highlight(25)}}} .
So the first 6 terms are: 0, 1, 2, 4, 11, 25 .