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 A209690 Triangle of coefficients of polynomials v(n,x) jointly generated with A209689; see the Formula section. 4
 1, 2, 1, 1, 4, 1, 1, 3, 7, 1, 1, 2, 9, 11, 1, 1, 2, 6, 22, 16, 1, 1, 2, 5, 19, 46, 22, 1, 1, 2, 5, 14, 54, 86, 29, 1, 1, 2, 5, 13, 42, 135, 148, 37, 1, 1, 2, 5, 13, 35, 124, 302, 239, 46, 1, 1, 2, 5, 13, 34, 99, 341, 617, 367, 56, 1, 1, 2, 5, 13, 34, 90, 287, 860, 1171 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Combinatorial limit of rows:  odd-indexed Fibonacci numbers.  For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+x*v(n-1,x), u(n,x)=x*u(n-1,x)+x*v(n-1,x), v(n,x)=u(n-1,x)+x*v(n-1,x)+1, EXAMPLE First five rows: 1 2...1 1...4...1 1...3...7...1 1...2...9...11...1 First three polynomials v(n,x): 1, 2 + x , 1 + 4x + x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x]; v[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1; Table[Expand[u[n, x]], {n, 1, z/2}] Table[Expand[v[n, x]], {n, 1, z/2}] cu = Table[CoefficientList[u[n, x], x], {n, 1, z}]; TableForm[cu] Flatten[%]   (* A209689 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A209690 *) CROSSREFS Cf. A209689, A208510. Sequence in context: A306846 A327315 A141450 * A061462 A294334 A122578 Adjacent sequences:  A209687 A209688 A209689 * A209691 A209692 A209693 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 12 2012 STATUS approved

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Last modified June 4 07:23 EDT 2020. Contains 334822 sequences. (Running on oeis4.)