a(n) = 6*binomial(n,4) + 3*binomial(n,3) + 4*binomial(n,2) - n + 2.

Terms

a(0) =1a(1) =4a(2) =14a(3) =40a(4) =97a(5) =206a(6) =394a(7) =694a(8) =1145a(9) =1792a(10) =2686a(11) =3884a(12) =5449a(13) =7450a(14) =9962a(15) =13066a(16) =16849a(17) =21404a(18) =26830a(19) =33232a(20) =40721a(21) =49414a(22) =59434a(23) =70910a(24) =83977a(25) =98776a(26) =115454a(27) =134164a(28) =155065a(29) =178322