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 A210211 Triangle of coefficients of polynomials u(n,x) jointly generated with A210212; see the Formula section. 3
 1, 2, 1, 3, 4, 1, 4, 8, 8, 1, 5, 14, 19, 16, 1, 6, 21, 42, 42, 32, 1, 7, 30, 72, 114, 89, 64, 1, 8, 40, 120, 216, 290, 184, 128, 1, 9, 52, 178, 414, 593, 706, 375, 256, 1, 10, 65, 260, 670, 1292, 1531, 1666, 758, 512, 1, 11, 80, 355, 1090, 2247, 3754, 3782 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row n starts with n and ends with 2^n followed by 1. n-th row sum: F(2k), where F=A000045 (Fibonacci numbers) Alternating row sums are signed products of two Fibonacci numbers. For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+v(n-1,x)+1, v(n,x)=u(n-1,x)+2x*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 2...1 3...4....1 4...8....8....1 5...14...19...16...1 First three polynomials u(n,x): 1, 2 + x, 3 + 4x + x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1; v[n_, x_] := u[n - 1, x] + 2 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[%]    (* A210211 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A210212 *) CROSSREFS Cf. A210204, A208510. Sequence in context: A180378 A208341 A201634 * A283054 A247358 A297224 Adjacent sequences:  A210208 A210209 A210210 * A210212 A210213 A210214 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 19 2012 STATUS approved

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Last modified October 19 21:01 EDT 2019. Contains 328225 sequences. (Running on oeis4.)