a(n) = 3^n-1+C(2n,n).

Terms

a(0) =1a(1) =4a(2) =14a(3) =46a(4) =150a(5) =494a(6) =1652a(7) =5618a(8) =19430a(9) =68302a(10) =243804a(11) =882578a(12) =3235596a(13) =11994922a(14) =44899568a(15) =169466426a(16) =644127110a(17) =2462746382a(18) =9462555788a(19) =36507525266a(20) =141333313220a(21) =548718227642