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 A210743 Triangle of coefficients of polynomials u(n,x) jointly generated with A210744; see the Formula section. 3
 1, 2, 3, 4, 8, 7, 7, 20, 25, 17, 12, 43, 76, 75, 41, 20, 88, 194, 264, 216, 99, 33, 172, 458, 770, 861, 606, 239, 54, 327, 1016, 2038, 2811, 2691, 1667, 577, 88, 608, 2161, 5012, 8206, 9689, 8149, 4517, 1393, 143, 1112, 4447, 11699, 22057, 30830 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row n starts with -1+F(n), where F=A000045 (Fibonacci numbers), and ends with A001333(n).  For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=2x*u(n-1,x)+(x+1)*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 2....3 4....8....7 7....20...25...17 12...43...76...75...41 First three polynomials u(n,x): 1, 2+ 3x, 4 + 8x + 7x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*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[%]      (* A210743 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]      (* A210744 *) CROSSREFS Cf. A210744, A208510. Sequence in context: A176077 A332778 A263694 * A210750 A036712 A036706 Adjacent sequences:  A210740 A210741 A210742 * A210744 A210745 A210746 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 24 2012 STATUS approved

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Last modified October 26 00:28 EDT 2020. Contains 338026 sequences. (Running on oeis4.)