discrete math. Solve the recursion relation

Question

Solve the recursion relation an = 2an−1 + 3an−2 + 4n + 4, a0 = 1, a1 = 1.

Answer 1

a0=1

a1=1

a2=2+3+4+4=13

a3=26+3+12+4=45

a4=90+39+16+4=149

a5=298+135+20+4=457

a6=914+447+24+4=1389

a7=2778+1371+28+4=4181

...

an=2an-1+3an-2+4an+4

1,1,13,45,149,457,1389,4181,...