Number of permutations p of (1,2,3,...,n) such that k+p(k) is a triangular number for 1<=k<=n.

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =0a(5) =1a(6) =1a(7) =1a(8) =2a(9) =4a(10) =3a(11) =9a(12) =14a(13) =13a(14) =52a(15) =124a(16) =161a(17) =181a(18) =715a(19) =2338a(20) =7073a(21) =8624a(22) =15466a(23) =52858a(24) =150365a(25) =316543a(26) =691771a(27) =1681604a(28) =5324919a(29) =15407311