a(n) = 2*a(n-1) + 3*a(n-2) + 5*a(n-3), a(0) = 3, a(1) = 2, a(2) = 10.

Terms

a(0) =3a(1) =2a(2) =10a(3) =41a(4) =122a(5) =417a(6) =1405a(7) =4671a(8) =15642a(9) =52322a(10) =174925a(11) =585026a(12) =1956437a(13) =6542577a(14) =21879595a(15) =73169106a(16) =244689882a(17) =818285057a(18) =2736485290a(19) =9151275161a(20) =30603431477a(21) =102343114887a(22) =342252900010