This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A209563 Triangle of coefficients of polynomials u(n,x) jointly generated with A209564; see the Formula section. 3
 1, 1, 1, 1, 3, 1, 1, 3, 6, 1, 1, 3, 8, 10, 1, 1, 3, 8, 19, 15, 1, 1, 3, 8, 21, 40, 21, 1, 1, 3, 8, 21, 53, 76, 28, 1, 1, 3, 8, 21, 55, 125, 133, 36, 1, 1, 3, 8, 21, 55, 142, 273, 218, 45, 1, 1, 3, 8, 21, 55, 144, 354, 554, 339, 55, 1, 1, 3, 8, 21, 55, 144, 375, 839, 1053 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A209563:  first k terms of row n are F(2),...,F(2k), where F = A000045 (Fibonacci numbers) and k=floor ((n+1)/2). A209564:  first k terms of row n are F(1), ..., F(2k-1), where k=floor ((n+2)/2). For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+v(n-1,x), v(n,x)=x*u(n-1,x)+x*v(n-1,x) +1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 1...1 1...3...1 1...3...6...1 1...3...8...10...1 First three polynomials v(n,x): 1, 1 + x, 1 + 3x + x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + v[n - 1, x]; v[n_, x_] := x*u[n - 1, x] + 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[%]   (* A209563 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A209564 *) CROSSREFS Cf. A209564, A208510. Sequence in context: A094644 A113046 A245541 * A308624 A133825 A156710 Adjacent sequences:  A209560 A209561 A209562 * A209564 A209565 A209566 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 10 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 23 16:14 EDT 2019. Contains 325258 sequences. (Running on oeis4.)