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%I #7 Nov 01 2022 13:01:30
%S 0,0,1,2,6,31,302,11706,3919531,47073195302,185055980038616706,
%T 8711901623180875318209094531,
%U 1612189902974799120179526719227635256224945302
%N a(n)=f(a(n-1)+1,a(n-2)+1,a(n-3)), 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], 1 + a[n - 2], a[n - 3]}]
%t Table[a[n], {n, 1, 16}] (* A203901 *)
%t nxt[{a_,b_,c_}]:={b,c,Total[Times@@@Subsets[{a,b+1,c+1},{2}]]}; NestList[nxt,{0,0,1},15][[All,1]] (* _Harvey P. Dale_, Nov 01 2022 *)
%Y Cf. A203761.
%K nonn
%O 1,4
%A _Clark Kimberling_, Jan 07 2012
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