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 A210560 Triangle of coefficients of polynomials v(n,x) jointly generated with A210559; see the Formula section. 4
 1, 3, 1, 5, 4, 2, 7, 9, 9, 3, 9, 16, 23, 16, 5, 11, 25, 46, 48, 30, 8, 13, 36, 80, 110, 101, 54, 13, 15, 49, 127, 215, 257, 203, 97, 21, 17, 64, 189, 378, 552, 570, 401, 172, 34, 19, 81, 268, 616, 1057, 1337, 1228, 776, 303, 55, 21, 100, 366, 948, 1862, 2772 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column 1: odd positive integers (A005408) Column 2: squares (A000290) Row n ends with F(n), where F=A000045 (Fibonacci numbers) Row sums: A005409 Alternating row sums: 1,2,3,4,5,6,7,8,...(A000027) 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)+1, v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 3...1 5...4...2 7...9...9...3 9...16...23...16...5 First three polynomials v(n,x): 1, 3 + x , 5 + 4x + 2x^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] + 1; v[n_, x_] := (x + 1)*u[n - 1, 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[%]  (* A210559 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]  (* A210560 *) CROSSREFS Cf. A210559, A208510. Sequence in context: A308676 A131809 A016574 * A208922 A209770 A210799 Adjacent sequences:  A210557 A210558 A210559 * A210561 A210562 A210563 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 22 2012 STATUS approved

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Last modified October 22 12:47 EDT 2019. Contains 328318 sequences. (Running on oeis4.)