A209151 - OEIS

%I #5 Mar 30 2012 18:58:15

%S 1,2,1,3,4,2,4,8,8,3,5,13,19,15,5,6,19,36,42,28,8,7,26,60,91,89,51,13,

%T 8,34,92,170,216,182,92,21,9,43,133,288,446,489,363,164,34,10,53,184,

%U 455,826,1105,1068,709,290,55,11,64,246,682,1414,2219,2619

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A208337; see the Formula section.

%C Last term in each row is a Fibonacci number (A000045).

%C Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...

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

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

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

%F where u(1,x)=1, v(1,x)=1.

%e First five rows:

%e 1

%e 2...1

%e 3...4....2

%e 4...8....8....3

%e 5...13...19...15...5

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

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

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

%t v[n_, x_] := x*u[n - 1, x] + 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[%]    (* A209151 *)

%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[%]    (* A208337 *)

%Y Cf. A208337, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 07 2012