A209760 - OEIS

%I #8 Mar 30 2012 18:58:15

%S 1,1,3,1,3,8,1,3,11,21,1,3,11,38,55,1,3,11,41,124,144,1,3,11,41,150,

%T 389,377,1,3,11,41,153,533,1187,987,1,3,11,41,153,568,1838,3549,2584,

%U 1,3,11,41,153,571,2084,6168,10447,6765,1,3,11,41,153,571,2128

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209759; see the Formula section.

%C Limiting row: A001835

%C Coefficient of x^n in v(n,x):  even-indexed Fibonacci numbers

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

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

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

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

%e First five rows:

%e 1

%e 1...3

%e 1...3...8

%e 1...3...11...21

%e 1...3...11...38...55

%e First three polynomials v(n,x): 1, 1 + 3x , 1 + 3x + 8x^2.

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

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

%t v[n_, x_] := x*u[n - 1, x] + 2 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[%]    (* A209759 *)

%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[%]    (* A209760 *)

%Y Cf. A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 14 2012