A208918 - OEIS

%I #5 Mar 30 2012 18:58:14

%S 1,1,4,1,4,12,1,4,16,40,1,4,20,64,128,1,4,24,88,240,416,1,4,28,112,

%T 368,896,1344,1,4,32,136,512,1504,3264,4352,1,4,36,160,672,2240,5952,

%U 11776,14080,1,4,40,184,848,3104,9472,23168,41984,45568,1,4,44

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208917; see the Formula section.

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

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

%F v(n,x)=2x*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...4

%e 1...4...12

%e 1...4...16...40

%e 1...4...20...64...128

%e First five polynomials v(n,x):

%e 1

%e 1 + 4x

%e 1 + 4x + 12x^2

%e 1 + 4x + 16x^2 + 40x^3

%e 1 + 4x + 20x^2 + 64x^3 + 128x^4

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

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

%t v[n_, x_] := 2 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[%]    (* A208917 *)

%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[%]    (* A208918 *)

%Y Cf. A208917, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 04 2012