Pell numbers A000129(n+1) (without P(0)) convoluted twice with itself.

Terms

a(0) =1a(1) =6a(2) =27a(3) =104a(4) =366a(5) =1212a(6) =3842a(7) =11784a(8) =35223a(9) =103122a(10) =296805a(11) =842160a(12) =2360780a(13) =6549240a(14) =18004980a(15) =49106992a(16) =132996957a(17) =357948894a(18) =957993823a(19) =2550977112a(20) =6761742234a(21) =17848312884a(22) =46932923478a(23) =122980461816