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 A193663 Q-residue of A049310 (triangle of coefficients of Fibonacci polynomials), where Q is the triangle given by t(n,k)=k+1 for 0<=k<=n.  (See Comments.) 2
 0, 1, 1, 9, 17, 80, 198, 748, 2107, 7236, 21680, 71279, 219879, 708436, 2215513, 7071210, 22256567, 70723367, 223272153, 708017329, 2238347440, 7091170416, 22433032016 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The definition of Q-residue is given at A193649. LINKS 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 Cf. A049310, A193649. Sequence in context: A151793 A118852 A118527 * A166705 A116526 A197396 Adjacent sequences:  A193660 A193661 A193662 * A193664 A193665 A193666 KEYWORD nonn AUTHOR Clark Kimberling, Aug 02 2011 STATUS approved

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Last modified September 28 03:03 EDT 2020. Contains 337392 sequences. (Running on oeis4.)