a(0) = 1, a(1) = 2, a(2) = 5; for n >= 3, a(n) = a(n-1) + 2*a(n-2) + a(n-3).

Terms

a(0) =1a(1) =2a(2) =5a(3) =10a(4) =22a(5) =47a(6) =101a(7) =217a(8) =466a(9) =1001a(10) =2150a(11) =4618a(12) =9919a(13) =21305a(14) =45761a(15) =98290a(16) =211117a(17) =453458a(18) =973982a(19) =2092015a(20) =4493437a(21) =9651449a(22) =20730338a(23) =44526673a(24) =95638798a(25) =205422482a(26) =441226751a(27) =947710513a(28) =2035586497a(29) =4372234274