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A193662 Q-residue of the Lucas triangle A114525, where Q is the triangle given by t(i,j)=1 for 0<=i<=j. (See Comments.)

%I A193662 #7 Feb 19 2015 14:23:51
%S A193662 2,1,5,7,25,51,149,351,945,2347,6125,15511,40009,102051,262085,670287,
%T A193662 1718625,4399771,11274269,28873351
%N A193662 Q-residue of the Lucas triangle A114525, where Q is the triangle given by t(i,j)=1 for 0<=i<=j.  (See Comments.)
%C A193662 For the definition of Q-residue, see A193649.
%F A193662 Conjecture: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) if n>3. - _R. J. Mathar_, Feb 19 2015
%t A193662 q[n_, k_] := 1;
%t A193662 r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}];
%t A193662 f[n_, x_] := LucasL[n, x];  (* A114525 *)
%t A193662 p[n_, k_] := Coefficient[f[n, x], x, k];
%t A193662 v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
%t A193662 Table[v[n], {n, 0, 16}]    (* A193662 *)
%t A193662 TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
%t A193662 Table[r[k], {k, 0, 8}]
%t A193662 TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, 4}]]
%Y A193662 Cf. A193649, A114525.
%K A193662 nonn
%O A193662 0,1
%A A193662 _Clark Kimberling_, Aug 02 2011