a(n) = a(n-1) + a(n-2) + (n+2)*binomial(n+3, 3)/2, with a(0) = 1, a(1) = 7.

Terms

a(0) =1a(1) =7a(2) =28a(3) =85a(4) =218a(5) =499a(6) =1053a(7) =2092a(8) =3970a(9) =7272a(10) =12958a(11) =22596a(12) =38739a(13) =65535a(14) =109714a(15) =182185a(16) =300620a(17) =493635a(18) =807555a(19) =1317360a(20) =2144396a(21) =3485032a(22) =5657028a(23) =9174560a(24) =14869613a(25) =24088399a(26) =39009168a(27) =63156437a(28) =102233030a(29) =165466347