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 A210563 Triangle of coefficients of polynomials u(n,x) jointly generated with A210564; see the Formula section. 3
 1, 1, 2, 1, 3, 5, 1, 3, 10, 13, 1, 3, 11, 32, 34, 1, 3, 11, 40, 99, 89, 1, 3, 11, 41, 141, 299, 233, 1, 3, 11, 41, 152, 482, 887, 610, 1, 3, 11, 41, 153, 556, 1604, 2595, 1597, 1, 3, 11, 41, 153, 570, 1998, 5217, 7508, 4181, 1, 3, 11, 41, 153, 571, 2113, 7042 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Last terms in rows: odd-indexed Fibonacci numbers Limiting row:  A001835 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)=(x+1)*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...5 1...3...10...13 1...3...11...32...34 First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 5x^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] + 1; v[n_, x_] := (x + 1)*u[n - 1, x] + 2 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[%]  (* A210563 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]  (* A210564 *) CROSSREFS Cf. A210564, A208510. Sequence in context: A089984 A284429 A062105 * A236311 A093412 A119355 Adjacent sequences:  A210560 A210561 A210562 * A210564 A210565 A210566 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 23 2012 STATUS approved

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)