a(n) = C(n+2, 2) + C(n+2, 3) + C(n+2, 4) + C(n+2, 5).

Terms

a(0) =1a(1) =4a(2) =11a(3) =26a(4) =56a(5) =112a(6) =210a(7) =372a(8) =627a(9) =1012a(10) =1573a(11) =2366a(12) =3458a(13) =4928a(14) =6868a(15) =9384a(16) =12597a(17) =16644a(18) =21679a(19) =27874a(20) =35420a(21) =44528a(22) =55430a(23) =68380a(24) =83655a(25) =101556a(26) =122409a(27) =146566a(28) =174406a(29) =206336