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