For a system I am studying the following sequence (which I would assume is quite common) came up: n1=1, n2=2, n3=4, n4=7, n5=11, n6=16, n7=22 .... i.e. the difference betweens two successive numbers grows with 1 as we move from (n_N-1, n_N) to (n_N,n_N+1). Is there a closed form expression f(k) for this sequence, i.e. f(1)=n1, f(2)=n2, f(3)=n3 etc. edit: So basically I have a sequence with I think what is called a recurence relation equal to: x_n+1 = x_n+n Can I find a closed form for this?