a(n) = a(n-1) + a(n-2) + F(n) - 1, a(0) = a(1) = 0, where F() = Fibonacci numbers A000045.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =3a(5) =8a(6) =18a(7) =38a(8) =76a(9) =147a(10) =277a(11) =512a(12) =932a(13) =1676a(14) =2984a(15) =5269a(16) =9239a(17) =16104a(18) =27926a(19) =48210a(20) =82900a(21) =142055a(22) =242665a(23) =413376a(24) =702408a(25) =1190808a(26) =2014608a(27) =3401833a(28) =5734251a(29) =9650312