login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209820 Triangle of coefficients of polynomials v(n,x) jointly generated with A209819; see the Formula section. 3

%I

%S 1,2,2,2,6,5,2,8,18,12,2,8,30,52,29,2,8,34,104,146,70,2,8,34,136,342,

%T 402,169,2,8,34,144,514,1080,1090,408,2,8,34,144,594,1848,3306,2920,

%U 985,2,8,34,144,610,2360,6370,9872,7746,2378,2,8,34,144,610,2552

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209819; see the Formula section.

%C Let T(n,k) be the general term.

%C T(n,n): A000129

%C T(n,n-1): 2*A071667

%C Row sums: A003462

%C Alternating row sums: 1,0,1,0,1,0,1,0,...

%C Limiting row: F(3), F(6),F(9),...where F=A000045 (Fibonacci numbers)

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

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

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

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

%e First five rows:

%e 1

%e 2...2

%e 2...6...5

%e 2...8...18...12

%e 2...8...30...52...29

%e First three polynomials v(n,x): 1, 2 + 2x , 2 + 6x + 5x^2.

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

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

%t v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%] (* A209819 *)

%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[%] (* A209820 *)

%Y Cf. A209819, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 23 2012

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 00:05 EST 2019. Contains 329106 sequences. (Running on oeis4.)