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Q-residue of A049310 (triangle of coefficients of Fibonacci polynomials), where Q=Pascal's triangle. (See Comments.)
3

%I #5 Mar 30 2012 18:57:38

%S 0,1,1,6,11,68,177,1215,4059,30733,124408,1027972,4862600,43450761,

%T 234283662,2247091674,13563976285,138780931929,925063455844,

%U 10044476018973,73144254450840,839146997933059,6618306039456419

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

%C The definition of Q-residue is given at A193649.

%t f[n_, x_] := Fibonacci[n, x];

%t q[n_, k_] := Coefficient[(x + 1)^n, x, k]; (* Pascal's triangle *)

%t r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}];

%t p[n_, k_] := Coefficient[f[n, x], x, k];

%t v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]

%t Table[v[n], {n, 0, 22}] (* A193664 *)

%t TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]

%t Table[r[k], {k, 0, 8}] (* A000110 *)

%t TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, n}]]

%Y Cf. A049310, A193649, A000110.

%K nonn

%O 0,4

%A _Clark Kimberling_, Aug 02 2011