A193664 Q-residue of A049310 (triangle of coefficients of Fibonacci polynomials), where Q=Pascal's triangle. (See Comments.)

0, 1, 1, 6, 11, 68, 177, 1215, 4059, 30733, 124408, 1027972, 4862600, 43450761, 234283662, 2247091674, 13563976285, 138780931929, 925063455844, 10044476018973, 73144254450840, 839146997933059, 6618306039456419

Offset: 0

Author

Clark Kimberling, Aug 02 2011

Keywords

• nonn

Comments

The definition of Q-residue is given at A193649.

Crossrefs

Cf. A049310, A193649, A000110.

Programs

Mathematica

f[n_, x_] := Fibonacci[n, x];
q[n_, k_] := Coefficient[(x + 1)^n, x, k]; (* Pascal's triangle *)
r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}];
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}]    (* A193664 *)
TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
Table[r[k], {k, 0, 8}]  (* A000110 *)
TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, n}]]