a(n) = 5*a(n-1) - 6*a(n-2) + a(n-3), with a(0)=1, a(1)=3, a(2)=8.

Terms

a(0) =1a(1) =3a(2) =8a(3) =23a(4) =70a(5) =220a(6) =703a(7) =2265a(8) =7327a(9) =23748a(10) =77043a(11) =250054a(12) =811760a(13) =2635519a(14) =8557089a(15) =27784091a(16) =90213440a(17) =292919743a(18) =951102166a(19) =3088205812a(20) =10027335807a(21) =32558546329a(22) =105716922615a(23) =343260670908