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A203761 a(n)=f(a(n-1)+1,a(n-2),a(n-3)), where f(x,y,z)=yz+zx+xy and a(1)=0, a(2)=0, a(3)=1.

%I A203761 #9 Jan 01 2013 12:01:51
%S A203761 0,0,1,0,1,2,3,14,81,1436,137649,208931366,29059416843159,
%T A203761 6075423684633064285934,176549538697128711514244195056431069,
%U A203761 1072613254042004122844787854494321338954112455109333945016
%N A203761 a(n)=f(a(n-1)+1,a(n-2),a(n-3)), where f(x,y,z)=yz+zx+xy and a(1)=0, a(2)=0, a(3)=1.
%C A203761 Sequences generated by similar recurrences and same initial values:
%C A203761 A203761......f(a(n-1)+1,a(n-2),a(n-3))
%C A203761 A203762......f(a(n-1),a(n-2)+1,a(n-3))
%C A203761 A203768......f(a(n-1),a(n-2),a(n-3)+1)
%C A203761 A203772......f(a(n-1),a(n-2)+1,a(n-3)+1)
%C A203761 A203900......f(a(n-1)+1,a(n-2),a(n-3)+1)
%C A203761 A203901......f(a(n-1)+1,a(n-2)+1,a(n-3))
%C A203761 A203902......f(a(n-1)+1,a(n-2)+1,a(n-3)+1)
%C A203761 Related sequences:
%C A203761 A121810 ... f(a(n-1),a(n-2),a(n-3)); a=(1,1,0,...). - _M. F. Hasler_, Jan 01 2013
%t A203761 a[1] = 0; a[2] = 0; a[3] = 1;
%t A203761 a[n_] := SymmetricPolynomial[2, {1 + a[n - 1], a[n - 2], a[n - 3]}]
%t A203761 Table[a[n], {n, 1, 16}]  (* A203761 *)
%Y A203761 Cf. A203902.
%K A203761 nonn
%O A203761 1,6
%A A203761 _Clark Kimberling_, Jan 07 2012