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 A209140 Triangle of coefficients of polynomials v(n,x) jointly generated with A209139; see the Formula section. 3
 1, 1, 3, 2, 5, 7, 3, 12, 18, 17, 5, 23, 51, 58, 41, 8, 45, 118, 189, 175, 99, 13, 84, 264, 506, 645, 507, 239, 21, 155, 558, 1268, 1950, 2085, 1428, 577, 34, 281, 1145, 2974, 5395, 6998, 6482, 3940, 1393, 55, 504, 2286, 6687, 13851, 21141, 23856 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Column 1:  Fibonacci numbers, A000045. Alternating row sums: (-2)^(n-1). For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x) = u(n-1,x) + (x+1)*v(n-1,x), v(n,x) = (x+1)*u(n-1,x) + x*v(n-1,x), where u(1,x)=1, v(1,x)=1. T(n,k) = T(n-1,k) + 2*T(n-1,k-1) + T(n-2,k) + T(n-2,k-2), T(1,0) = T(2,0) = 1, T(2,1) = 3, T(n,k) = 0 if k < 0 or if k >= n. - Philippe Deléham, Apr 11 2012 EXAMPLE First five rows:   1;   1,  3;   2,  5,  7;   3, 12, 18, 17;   5, 23, 51, 58, 41; First three polynomials v(n,x):   1   1 + 3x   2 + 5x + 7x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x]; v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x]; 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[%]    (* A209139 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A209140 *) CROSSREFS Cf. A209139, A208510. Sequence in context: A130295 A208613 A209584 * A265903 A006369 A097284 Adjacent sequences:  A209137 A209138 A209139 * A209141 A209142 A209143 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 05 2012 STATUS approved

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Last modified June 18 22:37 EDT 2021. Contains 345125 sequences. (Running on oeis4.)