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a(n)=f(a(n-1)+1,a(n-2),a(n-3)+1), where f(x,y,z)=yz+zx+xy and (a(1),a(2),a(3))=(0,0,1).
2

%I #6 Mar 30 2012 18:58:07

%S 0,0,1,2,7,36,391,17536,7520303,134830884224,1016333764230127711,

%T 137040823237740906153712364032,

%U 139279234211744145176797121311869355242595356863

%N a(n)=f(a(n-1)+1,a(n-2),a(n-3)+1), where f(x,y,z)=yz+zx+xy and (a(1),a(2),a(3))=(0,0,1).

%C For a guide to related sequences, see A203761.

%t a[1] = 0; a[2] = 0; a[3] = 1;

%t a[n_] := SymmetricPolynomial[2, {1 + a[n - 1], a[n - 2], 1 + a[n - 3]}]

%t Table[a[n], {n, 1, 16}] (* A203900 *)

%Y Cf. A203761.

%K nonn

%O 1,4

%A _Clark Kimberling_, Jan 07 2012