Number of one-sided n-step prudent walks, avoiding 4 or more consecutive east steps.

Terms

a(0) =1a(1) =3a(2) =7a(3) =17a(4) =40a(5) =96a(6) =229a(7) =547a(8) =1306a(9) =3119a(10) =7448a(11) =17786a(12) =42473a(13) =101426a(14) =242206a(15) =578390a(16) =1381200a(17) =3298317a(18) =7876408a(19) =18808927a(20) =44915872a(21) =107259471a(22) =256136497a(23) =611656057a(24) =1460639684a(25) =3488019553a(26) =8329419319a(27) =19890721694a(28) =47499206650