A210218 Triangle of coefficients of polynomials v(n,x) jointly generated with A210217; see the Formula section.

1, 1, 3, 1, 4, 7, 1, 4, 13, 15, 1, 4, 14, 38, 31, 1, 4, 14, 47, 103, 63, 1, 4, 14, 48, 151, 264, 127, 1, 4, 14, 48, 163, 462, 649, 255, 1, 4, 14, 48, 164, 544, 1348, 1546, 511, 1, 4, 14, 48, 164, 559, 1768, 3769, 3595, 1023, 1, 4, 14, 48, 164, 560, 1893, 5564

Offset: 1

Author

Clark Kimberling, Mar 19 2012

Keywords

• nonn
• tabl

Comments

Limiting row: A007070

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

Examples

			First five rows:
1
1...3
1...4...7
1...4...13...15
1...4...14...38...31
First three polynomials v(n,x): 1, 1 + 3x , 1 + 4x + 7x^2.
		

Crossrefs

Cf. A210217, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := x*u[n - 1, x] + 2 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[%]    (* A210217 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210218 *)

Formula

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

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

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