This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A209422 Triangle of coefficients of polynomials v(n,x) jointly generated with A209415; see the Formula section. 3
 1, 3, 5, 1, 9, 2, 1, 15, 6, 2, 1, 25, 13, 7, 2, 1, 41, 28, 16, 8, 2, 1, 67, 56, 38, 19, 9, 2, 1, 109, 109, 82, 49, 22, 10, 2, 1, 177, 206, 173, 112, 61, 25, 11, 2, 1, 287, 382, 352, 252, 146, 74, 28, 12, 2, 1, 465, 697, 701, 543, 347, 184, 88, 31, 13, 2, 1, 753, 1256, 1368, 1144, 784, 459, 226, 103, 34, 14, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For a discussion and guide to related arrays, see A208510. LINKS G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened FORMULA u(n,x) = x*u(n-1,x) + v(n-1,x), v(n,x) = u(n-1,x) + v(n-1,x) + 1, where u(1,x)=1, v(1,x)=1. G.f.: (1 + (1 - x)*t - t^2)/((1 - t)*(1 - (x + 1)*t + (x - 1)*t^2)) = 1 + 3*t + (5 + x)*t^2 + ... . - G. C. Greubel, Jan 03 2018 EXAMPLE First five rows:    1;    3;    5, 1;    9, 2, 1;   15, 6, 2, 1; First three polynomials v(n,x): 1, 3, 5 + x. 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_] := 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[%]    (* A209421 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A209422 *) CoefficientList[CoefficientList[Series[(1 + (1 - x)*t - t^2)/((1 - t)*(1 - (x + 1)*t + (x - 1)*t^2)), {t, 0, 10}], t], x]// Flatten (* G. C. Greubel, Jan 03 2018 *) CROSSREFS Cf. A209421, A208510. Sequence in context: A197326 A235605 A212695 * A320386 A112411 A283838 Adjacent sequences:  A209419 A209420 A209421 * A209423 A209424 A209425 KEYWORD nonn,tabf AUTHOR Clark Kimberling, Mar 09 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 October 16 08:15 EDT 2019. Contains 328051 sequences. (Running on oeis4.)