A209689 - OEIS

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

%S 1,0,2,0,2,3,0,1,6,4,0,1,4,13,5,0,1,3,13,24,6,0,1,3,9,35,40,7,0,1,3,8,

%T 28,81,62,8,0,1,3,8,22,82,167,91,9,0,1,3,8,21,64,217,315,128,10,0,1,3,

%U 8,21,56,188,519,554,174,11,0,1,3,8,21,55,155,529,1136,921

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209690; see the Formula section.

%C Combinatorial limit of rows:  even-indexed Fibonacci numbers. 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)=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 0...2

%e 0...2...3

%e 0...1...6...4

%e 0...1...4...13...5

%e First three polynomials v(n,x): 1, 2x, 2x + 3x^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_] := 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[%]    (* A209689 *)

%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[%]   (* A209690 *)

%Y Cf. A209690, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 12 2012