Number of multiplex juggling cards with n balls and capacity 3.

Terms

a(0) =1a(1) =2a(2) =7a(3) =24a(4) =70a(5) =198a(6) =532a(7) =1370a(8) =3418a(9) =8296a(10) =19677a(11) =45770a(12) =104687a(13) =235972a(14) =525136a(15) =1155516a(16) =2517199a(17) =5434454a(18) =11638099a(19) =24741812a(20) =52250956a(21) =109678746a(22) =228948036a(23) =475479494a(24) =982831024a(25) =2022696684a(26) =4145947065a(27) =8466032502a(28) =17226979885a(29) =34939008232