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 A210549 Triangle of coefficients of polynomials u(n,x) jointly generated with A210550; see the Formula section. 2
 1, 1, 2, 1, 3, 4, 1, 3, 9, 8, 1, 3, 10, 25, 16, 1, 3, 10, 33, 65, 32, 1, 3, 10, 34, 104, 161, 64, 1, 3, 10, 34, 115, 311, 385, 128, 1, 3, 10, 34, 116, 381, 886, 897, 256, 1, 3, 10, 34, 116, 395, 1224, 2421, 2049, 512, 1, 3, 10, 34, 116, 396, 1334, 3796, 6388 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Each row begins with 1 and ends with 2^(n-1). Row sums: 1,3,8,21,..., the even-indexed Fibonacci numbers For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1, v(n,x)=u(n-1,x)+2x*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 1...2 1...3...4 1...3...9....8 1...3...10...25...16 First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 4x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1; v[n_, x_] := (x + 1)*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[%]      (* A210235 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]      (* A210236 *) CROSSREFS Cf. A210550, A208510. Sequence in context: A027422 A135086 A210561 * A187002 A177226 A059026 Adjacent sequences:  A210546 A210547 A210548 * A210550 A210551 A210552 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 22 2012 STATUS approved

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Last modified October 20 12:47 EDT 2019. Contains 328257 sequences. (Running on oeis4.)