Number of protruded partitions of n with largest part at most 3.

Terms

a(0) =1a(1) =3a(2) =6a(3) =12a(4) =22a(5) =42a(6) =75a(7) =135a(8) =238a(9) =416a(10) =719a(11) =1236a(12) =2107a(13) =3574a(14) =6030a(15) =10130a(16) =16950a(17) =28267a(18) =46993a(19) =77916a(20) =128874a(21) =212701a(22) =350375a(23) =576165a(24) =945984a(25) =1551009a(26) =2539790a(27) =4154212a(28) =6787891a(29) =11081022