Diagonal sums of number triangle [k<=n]*C(n,2n-2k)3^(n-k)A000108(n-k).

Terms

a(0) =1a(1) =0a(2) =1a(3) =3a(4) =1a(5) =9a(6) =19a(7) =18a(8) =91a(9) =165a(10) =271a(11) =990a(12) =1765a(13) =3843a(14) =11467a(15) =21630a(16) =53299a(17) =140724a(18) =287119a(19) =736101a(20) =1818235a(21) =3982044a(22) =10225117a(23) =24521409a(24) =56584243a(25) =143641017a(26) =341948179a(27) =816095982a(28) =2045559205a(29) =4888806237