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

0,4

Comments

The definition of Q-residue is given at A193649.

Links

Table of n, a(n) for n=0..22.

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

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}]]

Crossrefs

Cf. A049310, A193649.

Sequence in context: A151793 A118852 A118527 * A166705 A116526 A197396

Adjacent sequences: A193660 A193661 A193662 * A193664 A193665 A193666

Keyword

nonn

Author

Clark Kimberling, Aug 02 2011

Status

approved