Solution to the Dancing School Problem with 3 girls and n+3 boys: f(3,n).

Terms

a(0) =1a(1) =4a(2) =14a(3) =36a(4) =76a(5) =140a(6) =234a(7) =364a(8) =536a(9) =756a(10) =1030a(11) =1364a(12) =1764a(13) =2236a(14) =2786a(15) =3420a(16) =4144a(17) =4964a(18) =5886a(19) =6916a(20) =8060a(21) =9324a(22) =10714a(23) =12236a(24) =13896a(25) =15700a(26) =17654a(27) =19764a(28) =22036a(29) =24476