Number of ascending runs in {1,...,3}^n.

Terms

a(0) =0a(1) =3a(2) =15a(3) =63a(4) =243a(5) =891a(6) =3159a(7) =10935a(8) =37179a(9) =124659a(10) =413343a(11) =1358127a(12) =4428675a(13) =14348907a(14) =46235367a(15) =148272039a(16) =473513931a(17) =1506635235a(18) =4778186031a(19) =15109399071a(20) =47652720147a(21) =149931729243a(22) =470715894135