OFFSET
0,4
COMMENTS
The definition of Q-residue is given at A193649.
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 02 2011
STATUS
approved