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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =11a(6) =26a(7) =65a(8) =164a(9) =421a(10) =1101a(11) =2912a(12) =7777a(13) =20957a(14) =56891a(15) =155418a(16) =426975a(17) =1178841a(18) =3269023a(19) =9101182a(20) =25428895a(21) =71279177a(22) =200391716a(23) =564899237a(24) =1596399798a(25) =4521769035a(26) =12835037619a(27) =36504130056a(28) =104012102095a(29) =296872273835