A210202 - OEIS

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

%S 1,2,3,4,7,6,7,17,17,12,12,35,50,40,24,20,70,120,135,92,48,33,134,275,

%T 365,346,208,96,54,251,593,930,1033,856,464,192,88,461,1236,2206,2874,

%U 2784,2064,1024,384,143,835,2500,5015,7389,8355,7240,4880

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210201; see the Formula section.

%C Column 1: F(n+2)-1, where F=A000045 (Fibonacci numbers)

%C Row sums: A048473

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

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

%F v(n,x)=(x+1)*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 2....3

%e 4....7....6

%e 7....17...17...12

%e 12...35...50...40...24

%e First three polynomials v(n,x): 1, 2 + 3x , 4 + 7x + 6x^2.

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

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

%t v[n_, x_] := (x + 1)*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[%]   (* A210201 *)

%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[%]   (* A210202 *)

%Y Cf. A210201, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 18 2012