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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210225 Triangle of coefficients of polynomials u(n,x) jointly generated with A210226; see the Formula section. 4

%I #4 Mar 30 2012 18:58:16

%S 1,2,1,3,5,1,4,12,10,1,5,22,36,17,1,6,35,88,87,26,1,7,51,175,277,181,

%T 37,1,8,70,306,680,734,338,50,1,9,92,490,1416,2196,1710,582,65,1,10,

%U 117,736,2632,5402,6156,3606,941,82,1,11,145,1053,4502,11592

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210226; see the Formula section.

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

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

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

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

%e First five rows:

%e 1

%e 2...1

%e 3...5....1

%e 4...12...10...1

%e 5...22...36...17...1

%e First three polynomials u(n,x): 1, 2 + x, 3 + 5x + x^2.

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

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

%t v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*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[%] (* A210225 *)

%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[%] (* A210226 *)

%Y Cf. A210226, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 20 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)