A193663 Q-residue of A049310 (triangle of coefficients of Fibonacci polynomials), where Q is the triangle given by t(n,k)=k+1 for 0<=k<=n. (See Comments.)

0, 1, 1, 9, 17, 80, 198, 748, 2107, 7236, 21680, 71279, 219879, 708436, 2215513, 7071210, 22256567, 70723367, 223272153, 708017329, 2238347440, 7091170416, 22433032016

Offset: 0

Author

Clark Kimberling, Aug 02 2011

Keywords

• nonn

Comments

The definition of Q-residue is given at A193649.

Crossrefs

Cf. A049310, A193649.

Programs

Mathematica

q[n_, k_] := k + 1;
r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}];
f[n_, x_] := Fibonacci[n, x]; (* A049310 *)
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, 22}]    (* A193663 *)
TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
Table[r[k], {k, 0, 8}]
TableForm[Table[p[n, k], {n, 0, 6}, {k, 0, n}]]

Formula

Conjecture: G.f.: x*(1-x+x^2) / ( 1-2*x-6*x^2+7*x^3+x^4 ). - R. J. Mathar, Feb 19 2015