The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A209699 Triangle of coefficients of polynomials u(n,x) jointly generated with A209700; see the Formula section. 3

%I #5 Mar 30 2012 18:58:15

%S 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,

%T 8,39,66,123,156,128,0,8,9,52,91,200,301,356,256,0,9,10,67,120,303,

%U 510,747,796,512,0,10,11,84,153,436,795,1356,1789,1764,1024,0,11

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209700; see the Formula section.

%C For a discussion and guide to related arrays, see A208510.

%F u(n,x)=x*u(n-1,x)+x*v(n-1,x),

%F v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,

%F where u(1,x)=1, v(1,x)=1.

%e First five rows:

%e 1

%e 0...2

%e 0...2...4

%e 0...3...4...8

%e 0...4...5...12...16

%e First three polynomials v(n,x): 1, 2x, 2x + 4x^2.

%t u[1, x_] := 1; v[1, x_] := 1; z = 16;

%t u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];

%t v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;

%t Table[Expand[u[n, x]], {n, 1, z/2}]

%t Table[Expand[v[n, x]], {n, 1, z/2}]

%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

%t TableForm[cu]

%t Flatten[%] (* A209699 *)

%t Table[Expand[v[n, x]], {n, 1, z}]

%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

%t TableForm[cv]

%t Flatten[%] (* A209700 *)

%Y Cf. A209700, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 12 2012

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

Last modified July 19 02:27 EDT 2024. Contains 374388 sequences. (Running on oeis4.)