login
Triangle of coefficients of polynomials v(n,x) jointly generated with A210549; see the Formula section.
3

%I #8 Mar 30 2012 18:58:16

%S 1,2,2,2,6,4,2,7,16,8,2,7,23,40,16,2,7,24,71,96,32,2,7,24,81,207,224,

%T 64,2,7,24,82,266,575,512,128,2,7,24,82,279,843,1535,1152,256,2,7,24,

%U 82,280,939,2572,3967,2560,512,2,7,24,82,280,955,3102,7565,9983

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210549; see the Formula section.

%C Row sums: -1+odd-indexed Fibonacci numbers

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

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

%e 2...2

%e 2...6...4

%e 2...7...16....8

%e 2...7...28....40...16

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

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

%t u[n_, x_] := x*u[n - 1, x] + 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[%] (* A210549 *)

%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[%] (* A210550 *)

%Y Cf. A210549, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 22 2012