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 A209572 Triangle of coefficients of polynomials v(n,x) jointly generated with A209571; see the Formula section. 3
 1, 1, 3, 1, 3, 5, 1, 3, 11, 7, 1, 3, 11, 29, 9, 1, 3, 11, 41, 61, 11, 1, 3, 11, 41, 129, 111, 13, 1, 3, 11, 41, 153, 339, 183, 15, 1, 3, 11, 41, 153, 523, 771, 281, 17, 1, 3, 11, 41, 153, 571, 1571, 1569, 409, 19, 1, 3, 11, 41, 153, 571, 2035, 4161, 2929, 571, 21 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Combinatorial limit of row n satisfies linear recurrence r(n)=4*r(n-1)-r(n-2) with r(1)=1 and r(2)=3.  For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+v(n-1,x), v(n,x)=2x*u(n-1,x)+x*v(n-1,x) +1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 1...3 1...3...5 1...3...11...7 1...3...11...29...9 First three polynomials v(n,x): 1, 1 + 3x , 1 + 3x + 5x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + v[n - 1, x]; v[n_, x_] := 2 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[%]   (* A209571 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A209572 *) CROSSREFS Cf. A209571, A208510. Sequence in context: A258208 A210952 A208523 * A134231 A225598 A126637 Adjacent sequences:  A209569 A209570 A209571 * A209573 A209574 A209575 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 11 2012 STATUS approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)