Number of Motzkin excursions of length n with an odd number of peaks.

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =4a(5) =10a(6) =25a(7) =62a(8) =159a(9) =414a(10) =1087a(11) =2886a(12) =7734a(13) =20878a(14) =56743a(15) =155154a(16) =426492a(17) =1177938a(18) =3267359a(19) =9098102a(20) =25423124a(21) =71268382a(22) =200371507a(23) =564861178a(24) =1596327999a(25) =4521633466a(26) =12834780857a(27) =36503642746a(28) =104011176114a(29) =296870510994