Number of weak peaks in all peakless Motzkin paths of length n.

Terms

a(0) =0a(1) =0a(2) =0a(3) =2a(4) =7a(5) =18a(6) =45a(7) =110a(8) =267a(9) =652a(10) =1602a(11) =3960a(12) =9845a(13) =24594a(14) =61689a(15) =155270a(16) =391962a(17) =991968a(18) =2515964a(19) =6393610a(20) =16275174a(21) =41491776a(22) =105922244a(23) =270734244a(24) =692756227a(25) =1774418286a(26) =4549173861a(27) =11672860634a(28) =29975156134a(29) =77029918152