a(n) = (a(n-1)+1)*(a(n-3)+1)/a(n-4) for n > 3, a(0) = a(1) = a(2) = a(3) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =4a(5) =10a(6) =22a(7) =115a(8) =319a(9) =736a(10) =3886a(11) =10816a(12) =24991a(13) =131989a(14) =367405a(15) =848947a(16) =4483720a(17) =12480934a(18) =28839196a(19) =152314471a(20) =423984331a(21) =979683706a(22) =5174208274a(23) =14402986300a(24) =33280406797a(25) =175770766825a(26) =489277549849