A210035 - OEIS

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

%S 1,3,6,2,11,6,4,19,16,12,8,32,36,36,24,16,53,76,88,80,48,32,87,152,

%T 204,208,176,96,64,142,294,444,520,480,384,192,128,231,554,932,1208,

%U 1280,1088,832,384,256,375,1024,1896,2704,3136,3072,2432,1792,768

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210036; see the Formula section.

%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)=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 3

%e 6....2

%e 11...6....4

%e 19...16...12...8

%e First three polynomials u(n,x): 1, 3, 6 + 2x.

%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_] := 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[%]    (* A210035 *)

%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[%]    (* A210036 *)

%Y Cf. A210036, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 16 2012