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 A210873 Triangle of coefficients of polynomials u(n,x) jointly generated with A210873; see the Formula section. 5
 1, 1, 2, 1, 1, 3, 1, 1, 3, 4, 1, 1, 2, 8, 5, 1, 1, 2, 6, 17, 6, 1, 1, 2, 5, 18, 31, 7, 1, 1, 2, 5, 14, 47, 51, 8, 1, 1, 2, 5, 13, 41, 107, 78, 9, 1, 1, 2, 5, 13, 35, 115, 218, 113, 10, 1, 1, 2, 5, 13, 34, 98, 296, 407, 157, 11, 1, 1, 2, 5, 13, 34, 90, 276, 695, 709, 211, 12 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Column 1: 1,1,1,1,1,1,1,1,1... Row sums: A083318 (1+2^n) Alternating row sums:  A137470 Limiting row:  1,1,2,5,13,34,..., odd-indexed Fibonacci numbers If the term in row n and column k is written as U(n,k), then U(n,n-1)=A105163. For a discussion and guide to related arrays, see A208510. LINKS FORMULA For a discussion and guide to related arrays, see A208510. u(n,x)=x*u(n-1,x)+v(n-1,x)-1, 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 six rows: 1 1...2 1...1...3 1...1...3....4 1...1...2....8...5 1...1...2....6...17...6 First three polynomials v(n,x): 1, 1 + 2x, 1 + x + 3x^2 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 14; u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] - 1; 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[%]    (* A210872 *) cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A210873 *) Table[u[n, x] /. x -> 1, {n, 1, z}]   (* A000225 *) Table[v[n, x] /. x -> 1, {n, 1, z}]   (* A083318 *) Table[u[n, x] /. x -> -1, {n, 1, z}]  (* -A077973 *) Table[v[n, x] /. x -> -1, {n, 1, z}]  (* A137470 *) CROSSREFS Cf. A210872, A208510. Sequence in context: A086599 A181846 A305499 * A224838 A030272 A157128 Adjacent sequences:  A210870 A210871 A210872 * A210874 A210875 A210876 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 29 2012 STATUS approved

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Last modified April 1 01:02 EDT 2020. Contains 333152 sequences. (Running on oeis4.)