a(n) is the n-th diagonal sum of left justified array T given by A027960.

Terms

a(0) =1a(1) =1a(2) =4a(3) =5a(4) =8a(5) =12a(6) =16a(7) =23a(8) =31a(9) =42a(10) =57a(11) =76a(12) =102a(13) =136a(14) =181a(15) =241a(16) =320a(17) =425a(18) =564a(19) =748a(20) =992a(21) =1315a(22) =1743a(23) =2310a(24) =3061a(25) =4056a(26) =5374a(27) =7120a(28) =9433a(29) =12497