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A193664 Q-residue of A049310 (triangle of coefficients of Fibonacci polynomials), where Q=Pascal's triangle.  (See Comments.) 3
0, 1, 1, 6, 11, 68, 177, 1215, 4059, 30733, 124408, 1027972, 4862600, 43450761, 234283662, 2247091674, 13563976285, 138780931929, 925063455844, 10044476018973, 73144254450840, 839146997933059, 6618306039456419 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 20 18:56 EDT 2019. Contains 326154 sequences. (Running on oeis4.)