Number of regions in an equilateral triangle "frame" of size n.

Terms

a(0) =1a(1) =12a(2) =75a(3) =249a(4) =543a(5) =1023a(6) =1746a(7) =2814a(8) =4293a(9) =6267a(10) =8868a(11) =12228a(12) =16464a(13) =21774a(14) =28176a(15) =35832a(16) =45066a(17) =56040a(18) =68931a(19) =84033a(20) =101307a(21) =120987a(22) =143574a(23) =169290a(24) =198222a(25) =230790a(26) =267117a(27) =307455a(28) =352437a(29) =402255