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 A209564 Triangle of coefficients of polynomials v(n,x) jointly generated with A209559; see the Formula section. 3
 1, 1, 2, 1, 2, 3, 1, 2, 5, 4, 1, 2, 5, 11, 5, 1, 2, 5, 13, 21, 6, 1, 2, 5, 13, 32, 36, 7, 1, 2, 5, 13, 34, 72, 57, 8, 1, 2, 5, 13, 34, 87, 148, 85, 9, 1, 2, 5, 13, 34, 89, 212, 281, 121, 10, 1, 2, 5, 13, 34, 89, 231, 485, 499, 166, 11, 1, 2, 5, 13, 34, 89, 233, 585, 1039 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A209563:  first k terms of row n are F(2), ..., F(2k), where F = A000045 (Fibonacci numbers) and k=floor ((n+1)/2). A209564:  first k terms of row n are F(1), ..., F(2k-1), where k=floor ((n+2)/2). For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+v(n-1,x), v(n,x)=x*u(n-1,x)+x*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 1...2 1...2...3 1...2...5...4 1...2...5...11...1 First three polynomials v(n,x): 1, 1+2x , 1+2x+3x^2 . MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + v[n - 1, x]; v[n_, x_] := 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[%]   (* A209563 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A209564 *) CROSSREFS Cf. A209563, A208510. Sequence in context: A064882 A065158 A181842 * A029653 A067763 A263683 Adjacent sequences:  A209561 A209562 A209563 * A209565 A209566 A209567 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 10 2012 STATUS approved

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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)