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.)

2, 1, 5, 7, 25, 51, 149, 351, 945, 2347, 6125, 15511, 40009, 102051, 262085, 670287, 1718625, 4399771, 11274269, 28873351

Offset: 0

Author

Clark Kimberling, Aug 02 2011

Keywords

• nonn

Comments

For the definition of Q-residue, see A193649.

Crossrefs

Cf. A193649, A114525.

Programs

Mathematica

q[n_, k_] := 1;
r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}];
f[n_, x_] := LucasL[n, x];  (* A114525 *)
p[n_, k_] := Coefficient[f[n, x], x, k];
v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
Table[v[n], {n, 0, 16}]    (* A193662 *)
TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
Table[r[k], {k, 0, 8}]
TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, 4}]]

Formula

Conjecture: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) if n>3. - R. J. Mathar, Feb 19 2015