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 A208519 Triangle of coefficients of polynomials v(n,x) jointly generated with A208518; see the Formula section. 3
 1, 2, 2, 3, 5, 3, 4, 9, 11, 5, 5, 14, 26, 23, 8, 6, 20, 50, 65, 45, 13, 7, 27, 85, 145, 150, 86, 21, 8, 35, 133, 280, 385, 329, 160, 34, 9, 44, 196, 490, 840, 952, 692, 293, 55, 10, 54, 276, 798, 1638, 2310, 2232, 1413, 529, 89, 11, 65, 375, 1230, 2940, 4956 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS coefficient of x^(n-1): Fibonacci(n+1) = A000045(n+1) col 1:  A000027 col 2:  A000096 col 3:  A051925 row sums:  A002878 (bisection of Lucas sequence) alternating row sums:  A000045(n-2), Fibonacci numbers LINKS FORMULA u(n,x)=u(n-1,x)+x*v(n-1,x), v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 2...2 3...5....3 4...9....11...5 5...14...26...23...8 First five polynomials v(n,x): 1 2 + 2x 3 + 5x + 3x^2 4 + 9x + 11x^2 + 5x^3 5 + 14x + 26x^2 + 23x^3 + 8x^4 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + x*v[n - 1, x]; v[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%]   (* A208518 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A208519 *) CROSSREFS Cf. A208518. Sequence in context: A124727 A210565 A125101 * A210232 A047666 A285935 Adjacent sequences:  A208516 A208517 A208518 * A208520 A208521 A208522 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Feb 28 2012 STATUS approved

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Last modified October 23 05:56 EDT 2019. Contains 328335 sequences. (Running on oeis4.)