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 A209689 Triangle of coefficients of polynomials u(n,x) jointly generated with A209690; see the Formula section. 3
 1, 0, 2, 0, 2, 3, 0, 1, 6, 4, 0, 1, 4, 13, 5, 0, 1, 3, 13, 24, 6, 0, 1, 3, 9, 35, 40, 7, 0, 1, 3, 8, 28, 81, 62, 8, 0, 1, 3, 8, 22, 82, 167, 91, 9, 0, 1, 3, 8, 21, 64, 217, 315, 128, 10, 0, 1, 3, 8, 21, 56, 188, 519, 554, 174, 11, 0, 1, 3, 8, 21, 55, 155, 529, 1136, 921 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Combinatorial limit of rows: even-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), v(n,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 0...2 0...2...3 0...1...6...4 0...1...4...13...5 First three polynomials v(n,x): 1, 2x, 2x + 3x^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. A209690, A208510. Sequence in context: A323474 A132814 A058623 * A204329 A111565 A299761 Adjacent sequences: A209686 A209687 A209688 * A209690 A209691 A209692 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 12 2012 STATUS approved

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Last modified March 23 00:55 EDT 2023. Contains 361434 sequences. (Running on oeis4.)