The number of Motzkin paths of length n satisfying the red-blue rule.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =6a(6) =11a(7) =23a(8) =47a(9) =103a(10) =225a(11) =513a(12) =1173a(13) =2761a(14) =6529a(15) =15767a(16) =38265a(17) =94359a(18) =233795a(19) =586590a(20) =1478265a(21) =3763290a(22) =9619065a(23) =24792705a(24) =64135965a(25) =167078577a(26) =436693431a(27) =1148208090a(28) =3028075677a(29) =8026793118