a(n) = 3*(3^(n-1) - 2^n + 1)/2 - binomial(n,2), n >= 3.

Terms

a(0) =0a(1) =12a(2) =65a(3) =255a(4) =882a(5) =2870a(6) =9039a(7) =27945a(8) =85448a(9) =259512a(10) =784797a(11) =2366819a(12) =7125198a(13) =21424938a(14) =64373339a(15) =193316877a(16) =580344132a(17) =1741819148a(18) =5227030665a(19) =15684238119a(20) =47059006250a(21) =141189602142a(22) =423593972775