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

0,4

Comments

The definition of Q-residue is given at A193649.

Links

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

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}]]

Crossrefs

Cf. A049310, A193649, A000110.

Sequence in context: A305608 A128387 A061519 * A080875 A001543 A077705

Adjacent sequences: A193661 A193662 A193663 * A193665 A193666 A193667

Keyword

nonn

Author

Clark Kimberling, Aug 02 2011

Status

approved