a(n) = Sum_{k=1..n} k^2 * 4^(n-k).

Terms

a(0) =0a(1) =1a(2) =8a(3) =41a(4) =180a(5) =745a(6) =3016a(7) =12113a(8) =48516a(9) =194145a(10) =776680a(11) =3106841a(12) =12427508a(13) =49710201a(14) =198841000a(15) =795364225a(16) =3181457156a(17) =12725828913a(18) =50903315976a(19) =203613264265a(20) =814453057460