A210878 Triangle of coefficients of polynomials u(n,x) jointly generated with A210879; see the Formula section.

1, 0, 3, 0, 4, 7, 0, 2, 14, 17, 0, 2, 12, 46, 41, 0, 2, 8, 54, 140, 99, 0, 2, 8, 42, 212, 408, 239, 0, 2, 8, 34, 200, 758, 1154, 577, 0, 2, 8, 34, 160, 866, 2544, 3194, 1393, 0, 2, 8, 34, 144, 754, 3448, 8154, 8696, 3363, 0, 2, 8, 34, 144, 642, 3400, 12850

Offset: 1

Author

Clark Kimberling, Mar 30 2012

Keywords

• nonn
• tabl

Comments

Leading coefficient of u(n,x): A001333

Limiting row: 0,2,8,34,144,610,...(Fibonacci numbers)

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

Examples

			First six rows:
1
0...3
0...4...7
0...2...14...17
0...2...12...46...41
0...2...8....54...140...99
First three polynomials u(n,x): 1, 3x, 4x + 7x^2.
		

Crossrefs

Cf. A210879, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 14;
u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A210878 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210879 *)

Formula

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

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

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