A210195 - OEIS

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

%S 1,3,5,4,7,12,8,9,24,32,16,11,40,80,80,32,13,60,160,240,192,64,15,84,

%T 280,560,672,448,128,17,112,448,1120,1792,1792,1024,256,19,144,672,

%U 2016,4032,5376,4608,2304,512,21,180,960,3360,8064,13440,15360

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210196; see the Formula section.

%C Row sums:  powers of 3

%C Periodic alternating row sums: 1,3,1,3,1,3,1,3,...

%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)=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 3

%e 5...4

%e 7...12...8

%e 9...24...32...16

%e First three polynomials u(n,x): 1, 3, 5 + 4x.

%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_] := 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[%]   (* A210195 *)

%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[%]   (* A210196 *)

%Y Cf. A210196, A208510.

%K nonn,tabf

%O 1,2

%A _Clark Kimberling_, Mar 18 2012