Number of three-choice paths along a corridor of height 5, starting from the lower side.

Terms

a(0) =1a(1) =2a(2) =5a(3) =13a(4) =35a(5) =96a(6) =266a(7) =741a(8) =2070a(9) =5791a(10) =16213a(11) =45409a(12) =127206a(13) =356384a(14) =998509a(15) =2797678a(16) =7838801a(17) =21963661a(18) =61540563a(19) =172432468a(20) =483144522a(21) =1353740121a(22) =3793094450a(23) =10628012915a(24) =29779028189a(25) =83438979561a(26) =233790820762a(27) =655067316176