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 A209699 Triangle of coefficients of polynomials u(n,x) jointly generated with A209700; see the Formula section. 3
 1, 0, 2, 0, 2, 4, 0, 3, 4, 8, 0, 4, 5, 12, 16, 0, 5, 6, 19, 28, 32, 0, 6, 7, 28, 45, 68, 64, 0, 7, 8, 39, 66, 123, 156, 128, 0, 8, 9, 52, 91, 200, 301, 356, 256, 0, 9, 10, 67, 120, 303, 510, 747, 796, 512, 0, 10, 11, 84, 153, 436, 795, 1356, 1789, 1764, 1024, 0, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For a discussion and guide to related arrays, see A208510. LINKS Table of n, a(n) for n=1..68. FORMULA u(n,x)=x*u(n-1,x)+x*v(n-1,x), v(n,x)=2x*u(n-1,x)+v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 0...2 0...2...4 0...3...4...8 0...4...5...12...16 First three polynomials v(n,x): 1, 2x, 2x + 4x^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]; v[n_, x_] := 2 x*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[%] (* A209699 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%] (* A209700 *) CROSSREFS Cf. A209700, A208510. Sequence in context: A199335 A141660 A368500 * A115273 A194759 A209697 Adjacent sequences: A209696 A209697 A209698 * A209700 A209701 A209702 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 12 2012 STATUS approved

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Last modified June 18 10:36 EDT 2024. Contains 373479 sequences. (Running on oeis4.)